The advantage of having a blowhole on top of a dolphin's head is that it allows them to breathe while swimming without having to break the surface of the water, which is crucial for their survival.
Dolphins are aquatic mammals and need to breathe air to survive. The location of their blowhole on the top of their head allows them to take in air without having to break the surface of the water, which is critical for their survival in the wild. When a dolphin needs to breathe, it can simply surface and quickly exhale and inhale through its blowhole.
This enables them to maintain a constant speed while swimming, and also helps them avoid detection from predators or prey that may be lurking at the surface. In addition, having a blowhole on top of their head allows them to quickly clear their airways of water and mucus, which can be useful for diving and hunting.
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What is the current moving through a wire that has 0. 60 C of electrons passing through a point in 1. 5 min?
The current moving through a wire that has 0. 60 C of electrons passing through a point in 1. 5 min is 0.4 Amps (A).
The current is 0.4 Amps (A),
It is calculated using the formula
I = Q/t,
= 0.60/1.5
= 0.4 Amps
where Q is the charge (Coulombs) of electrons and t is the time (seconds) taken for them to pass through the point.
The positive sign for current corresponds to the direction a positive charge would move. In metal wires, current is carried by negatively charged electrons, so the positive current arrow points in the opposite direction the electrons move.
In fact, an electric current is defined as the net movement of charge(s). This includes slow drift of electrons inside a wire, or a stream of electrons, protons, or muons traveling near light speed through the vacuum inside a particle accelerator.
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the frequency of a wave is doubled when the wavelength remains the same. what happens to the speed of the wave? group of answer choices it is cut to one-fourth it doubles it quadruples remains unchanged
The speed of the wave remains unchanged.
The speed of a wave is determined by the product of its wavelength and frequency. This can be represented by the formula: speed = wavelength x frequency
If the frequency of a wave is doubled while the wavelength remains the same, then the product of the wavelength and frequency will remain constant. This means that the speed of the wave will also remain constant.
To understand this, let's consider an example:
Suppose the original frequency of a wave is f, and its wavelength is λ. Then, the speed of the wave is given by:
speed = λ x f
Now, if the frequency is doubled, the new frequency becomes 2f. The wavelength remains the same at λ. So, the new speed of the wave can be calculated as: new speed = λ x 2f = 2(λ x f) = 2 x speed
As we can see, the new speed is twice the original speed, which contradicts our assumption that the speed remains constant. Therefore, the speed of the wave remains unchanged when the frequency is doubled while the wavelength remains the same.
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why is mcb is better than fuse
Answer:
MCB (Miniature Circuit Breaker) is generally considered better than fuses for several reasons:
Cost-effective: MCBs are more cost-effective in the long run compared to fuses as they can be reset and reused after tripping, whereas fuses need to be replaced each time they blow.
Convenience: MCBs can be reset with the flip of a switch, while fuses need to be manually replaced, which can be a hassle.
Accuracy: MCBs are more accurate in protecting against overloading and short circuits. They can be set to trip at specific amperages, providing better protection against damage to electrical appliances and wiring.
Safety: MCBs are safer than fuses as they do not produce arc flashes during tripping, which can cause electrical fires or explosions.
Overall, MCBs are a more efficient and safer alternative to fuses for protecting electrical circuits.
Explanation:
you have a camera with a 35.0-mm-focal-length lens and 36.0-mm-wide film. you wish to take a picture of a 12.0-m-long sailboat but find that the image of the boat fills only of the width of the film. (a) how far are you from the boat? (b) how much closer must the boat be to you for its image to fill the width of the film?
The distance between the boat and the camera is 0.0525 m. The boat must move closer by a distance of 35 mm to fill the width of the film.
you have a camera with a 35.0-mm-focal-length lens and 36.0-mm-wide film. you wish to take a picture of a 12.0-m-long sailboat but find that the image of the boat fills only the width of the film.
(a) Given data:
The focal length of the lens, f = 35.0 mm
Width of the film, w = 36.0 mm
Length of the sailboat, L = 12.0 m
Length of the image of the sailboat on film = Width of the film
Let the distance between the boat and the camera be x.
The object distance, u = ?
Image distance, v = f
Let M be the magnification of the image, then we have:
M = v/u
Width of the image, W' = w
Since the image of the boat fills only half of the width of the film,
W' = w/2.
Now, using the relation,
1/f = 1/u + 1/v
Putting f = 35mm, v = 35mm, and solving for u, we get
u = 52.5 mm = 0.0525 m
Therefore, the distance between the boat and the camera is 0.0525 m.
(b)Width of the image, W = w = 36 mm
Width of the sailboat, L = 12 m
Let the new distance between the boat and the camera be y.
The new image distance, v' = f
The new object distance, u' =?We know that the magnification of the image is given by M = v'/u'.
And the width of the image of the boat is given by:
W = (M)(L)
Using the relation,
1/f = 1/u' + 1/v', we can find the object distance, u'.
Substituting the given values, we get
u' = 0.0175 m = 17.5 mm
Therefore, the boat must move closer by a distance of (52.5 - 17.5) mm = 35 mm to fill the width of the film.
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Drive north on a s You straight two lane road at constant 88km/h. A truck in the other lane approaches you at a constant 104km/h. Find (a) the truck's velocity relative to you and (b) your velocity relative to the truck. (c) How do the relative velocities ties changes after you and the truck pass each other?
(a) To find the truck's velocity relative to you, we need to subtract your velocity from the truck's velocity.
Since you are driving north and the truck is approaching you in the other lane, the velocities are in opposite directions. Therefore, we can simply subtract the two speeds: Truck's velocity relative to you = Truck's velocity - Your velocity = 104 km/h - 88 km/h = 16 km/h north (since the truck is approaching you). Therefore, the truck's velocity relative to you is 16 km/h north. (b) To find your velocity relative to the truck, we need to subtract the truck's velocity from your velocity. Since you are driving north and the truck is approaching you from the opposite direction, the velocities are again in opposite directions. Therefore, we can simply subtract the two speeds: Your velocity relative to the truck = Your velocity - Truck's velocity = 88 km/h - 104 km/h = -16 km/h north (since you are moving away from the truck). Therefore, your velocity relative to the truck is 16 km/h south. (c) After you and the truck pass each other, the relative velocities change. The truck is now moving away from you, and you are moving away from the truck. Therefore, the velocity of the truck relative to you will decrease, while your velocity relative to the truck will increase. However, the magnitude of the relative velocities will remain the same, since the difference between the two velocities is still 16 km/h. The direction of the relative velocities will also change, with the truck's velocity relative to you now being 16 km/h south, and your velocity relative to the truck now being 16 km/h north.
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(PLS HELP ME NOW!!!!!) Ospreys are birds that eat fish. Where would an osprey MOST likely live?
A.
near a forest
B.
near a marsh
C.
near a desert
D.
near a prairie
A converging lens forms a real image of an object. if magnification is 2 and the distance between the image and the object is 90.0cm; determine the
(i) Focal length of the lens
(ii) Distance for which the image would be the same size as the object.
(I) The focal length of the lens is 180.0 cm.
(II) The distance for which the image would be the same size as the object is 90.0 cm.
What is the focal length of the lens?We can use the lens equation and the magnification formula to solve for the focal length of the lens and the distance for which the image would be the same size as the object.
The lens equation is:
1/f = 1/do + 1/di
where;
f is the focal length of the lens, do is the distance between the object and the lens, and di is the distance between the image and the lens.We are given that the distance between the image and the object is 90.0 cm and the magnification is 2. The magnification formula is:
m = - di/do
where;
m is the magnification.Substituting these values into the magnification formula, we get:
2 = - di/do
di = -2do
Substituting these values into the lens equation, we get:
1/f = 1/do - 1/2do
Simplifying this equation, we get:
1/f = 1/2do
f = 2do
Substituting the given value of di, we get:
f = 2(-90.0 cm) = -180.0 cm
Since the focal length must be positive for a converging lens, we take the absolute value and get:
f = 180.0 cm
(ii) Distance for which the image would be the same size as the object:
When the image is the same size as the object, the magnification is 1. We can use the magnification formula to solve for the distance di:
m = - di/do
1 = - di/do
di = -do
Substituting the given value of do, we get:
di = -90.0 cm
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If you are traveling at 50 mph, how many minutes will it take to travel 10 km?
( 1 mile = 1. 6 kilometer )
To calculate time, divide the distance by speed. hence, the time is 7.5 minutes.
Divide the distance by the speed to find the passing duration. Multiply the speed by the duration to get the distance. These formulae can be represented more simply as s=d/t, where s stands for speed, d for distance, and t for time.
Given: speed= 50 mph.
distance= 10km
1 mile = 1.6 km
1km = 1/1.6 miles= 0.625 milesmiles
We know that, time= distance/speedspeed
Time = 0.625*10/50= 0.125 hours.
1 hour = 60 minutes
hence, 0.125 hours= 60*0.125 = 7.5 minutes.
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You use a rope and pulley system with an ideal mechanical advantage of 2.00. How big of an output load can you lift with an input
force of 200 N?
When two rope segments pull up on the load in the single movable pulley, the optimal mechanical advantage is 2. This sort of pulley does not change the direction of the applied force, but it does increase it by a factor of two.
What is the ideal mechanical advantage?There are two methods for calculating a pulley system's mechanical advantage.
The mechanical advantage may be calculated simply by counting the number of falls (or active lifting ropes) that are really attached to the load. You may also split the effort distance by the load distance.
Assuming an ideal rope and pulley system with a mechanical advantage of [tex]2.00[/tex] , the output load that can be lifted with an input force of [tex]200 N[/tex] can be calculated using the formula:
Output force = Input force x Mechanical advantage
Where the mechanical advantage is given as [tex]2.00[/tex] .
Thus, the output force is:
Output force [tex]= 200 N \times 2.00 = 400 N[/tex]
Therefore, with an input force of [tex]200 N[/tex] , the rope and pulley system can lift an output load of up to [tex]400 N[/tex] .
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The distance traveled by an object per unit time is called
The distance an object travels in a unit of time is called the speed of the object. SI. the unit of speed is meter per second (ms−1).
Speed is measured in relation to distance compared to the time it took to cover the distance. Speed is a scalar quantity because it only has direction and not magnitude. There are four types of speeds and they are:
Even speed
Variable speed
Average speed
Instantaneous speed
Constant velocity: An object is at a constant velocity when the object travels the same distance in equal intervals of time.
Variable speed: an object is said to have variable speed when the object travels varying distances at regular intervals.
Average speed: Average speed is defined as the constant speed obtained by the ratio of the total distance traveled by the object to the total time spent on the object. Instantaneous velocity: When an object is moving with a variable velocity, the velocity of that object at any instant of time is called instantaneous velocity.
Speed measurement
A speedometer is used to measure the speed of vehicles. An odometer is used to measure the distance traveled. Speed can also be calculated using a gragraphph. A distance-time graph helps to understand the speed of an object.
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Yellow,,white,,absorbs,,reflects ,,wavelengths. The color of an object has to do with the light ________ That are reflected from the object. A white t-shirt looks _______ because it _____ all the colors while black ______ all the wavelengths of light. A ripe mango is yellow because when white light hits it ,its atomic imards reflect all the _________ wavelengths more than the other colors and bounce them at our eyes.
The color of an object has to do with the light wavelength. A white t-shirt looks yellow because it absorbs all the colors while black white all the wavelengths of light. A ripe mango is yellow because reflect all the reflects wavelengths.
The light wavelength has an impact on an object's color of which the object reflects. Because it absorbs all hues, a white t-shirt seems yellow, but a black one emits all light wavelengths. A ripe mango appears yellow because, when white light strikes it, its atomic impurities bounce all the wavelengths of light at our sight more than the other colors.
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. Is it possible to make a steel bar into a magnet? If so, explain
the method.
Answer:
yes if you can only install a magnetic force into the bar
Police radar guns (Figure 1) work by measuring the change in frequency of a reflected pulse of electromagnetic waves. A gun reads correctly only if a car is moving directly toward or away from the person making the measurement.
The following are the answers to the following questions:
There will not be a Doppler shift.
There will still be a Doppler shift observed by the radar gun.
What exactly is Doppler shift?Doppler shift is the change in frequency of a wave caused by relative motion between the source and the observer. This shift in frequency can be used to calculate the relative motion of the source and observer and is employed in a variety of applications such as radar, astronomy, and medical imaging.
1: The guns are adjusted for forward or backward motion towards or away from the gun. What happens if an automobile moves perpendicular to the gun's line of sight?
The radar gun will not detect any Doppler shift.
2: If the car is approaching or departing from a different angle, there is .
A Doppler change will still be detected, but it will be less than the maximum Doppler shift that would occur if the car moved directly towards or away from the gun.
3: As a result, if the radar gun indicates that a car is driving at a specific speed, the car is moving at the speed radar report.
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calculate the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s. (b) what is unreasonable about the result? (c) which premises are unreasonable or inconsistent?
A-the minimum coefficient of friction is 0.18 ,B- it is unreasonable, C-no premises is inconsistent.
(a) Calculation of the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s: A car moving with a velocity of 30.0 m/s in a circular path of radius 50.0 m negotiates an unbanked curve. Hence, the force required to move a car in a circular path is the frictional force between the wheels of the car and the road.
The minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s is given by:μmin = tanθ= v² / rgWhere,μmin is the minimum coefficient of frictionv is the velocity of the carr is the radius of the curveg is the acceleration due to gravity θ is the angle of banking.
As the curve is unbanked, the angle of banking is 0°.∴ μmin = v² / rg= (30.0 m/s)² / (50.0 m × 9.81 m/s²)= 0.183 or 0.18 (approx)
(b)The result of 0.18 is not unreasonable.
(c) None of the premises is unreasonable or inconsistent.
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shows a map of Olivia's trip to a coffee shop. She gets on her bike at Loomis and then rides south 0.9mi to Broadway. She turns east onto Broadway, rides 0.8 mi to where Broadway turns, and then continues another 1.4mi to the shop.
What is the magnitude of the total displacement of her trip?
What is the direction of the total displacement of her trip?
The magnitude of the total displacement of Olivia's trip is 1.9 miles. The direction of the total displacement of her trip is southeast.
To find the magnitude of the total displacement, we need to use the Pythagorean theorem:
a^2 + b^2 = c^2
In this case, a = 0.9 miles (the distance she travels south), and b = 0.8 + 1.4 = 2.2 miles (the distance she travels east).
Plugging in these values, we get:
0.9^2 + 2.2^2 = c^2
0.81 + 4.84 = c^2
5.65 = c^2
c = √5.65
c = 2.376
So the magnitude of the total displacement is approximately 2.376 miles.
To find the direction of the total displacement, we need to use the tangent function:
tan θ = opposite/adjacent
In this case, opposite = 2.2 miles (the distance she travels east), and adjacent = 0.9 miles (the distance she travels south).
Plugging in these values, we get:
tan θ = 2.2/0.9
θ = tan^-1(2.2/0.9)
θ = 67.38 degrees
So the direction of the total displacement is approximately 67.38 degrees from south, or southeast.
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A point charge (q1) has a magnitude of 3x10-6 C. A second charge (q2) has a magnitude of -1. 5x10-6 C and is located 0. 12 m from the first charge. Determine the electrostatic force each charge exerts on the other
The electrostatic force each charge exerts on the other is 2.81N .[tex]q_{1} =[/tex] [tex]3[/tex] × [tex]10^{-6} C[/tex][tex]\\q_2}[/tex] [tex]= - 1.5[/tex] × [tex]10^{-6} C[/tex] They are separated by a distance [tex]r = 0.12m[/tex]
Electrostatic force is [tex]F =[/tex] [tex]\frac{kq_{1} q_{2} }{r^{2} }[/tex]
[tex]F = 2.81N[/tex]
The term "scalar" refers to a category of quantities that may be fully defined by a single magnitude. Quantities called vectors can be fully represented by their direction as well as their magnitude.
How do you define a vector's magnitude?
A vector's length is considered to be its magnitude. The letter "a" stands for the dynamic array magnitude. For further information about a vector's magnitude, go to its introduction. This article deduces formulas for vectors magnitude in considerations of their coordinates in three and two dimensions, respectively.
Magnitude is simply "distance or amount," according to the definition given in physics. It illustrates the either the absolute or relative size or velocity direction for an item.
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A child in danger of drowning in a river is being carried downstream by a current that flows uniformly with a speed of 2.0 m/s. The child is 200 m away from the show and 1500 m upstream of the boat dock from which the rescue team sets out. If their boat speed is 8.0 m/s with respect to the water, at what angle should the pilot leave the shore to go directly to the child?
The pilot should leave the shore at an angle of 14.04° in order to go directly to the child.
To find the angle, we can use the Pythagorean Theorem and trigonometry.
First, we need to find the distance between the child and the boat dock. Using the Pythagorean Theorem, we get:
d = √((200 m)^2 + (1500 m)^2) = 1520.69 m
Next, we need to find the time it will take for the child to reach the boat dock. Since the child is being carried by the current at a speed of 2.0 m/s, we can use the formula:
t = d/v = 1520.69 m / 2.0 m/s = 760.34 s
Now, we need to find the distance the boat will travel in this time. Since the boat has a speed of 8.0 m/s with respect to the water, we can use the formula:
d = v*t = 8.0 m/s * 760.34 s = 6082.72 m
Finally, we can use trigonometry to find the angle at which the pilot should leave the shore. Using the formula:
tan(θ) = opposite/adjacent = 200 m / 6082.72 m = 0.0329
θ = tan^-1(0.0329) = 14.04°
Therefore, the pilot should leave the shore at an angle of 14.04° in order to go directly to the child.
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whats the total mass of 100 g of viniger and 10 g of baking soda show the calculations
super mario, spying a mystery block just ahead and wanting star power, takes a running leap towards the block, which is a distance of 8.2 m above mario's head. the acceleration due to gravity in the mushroom kingdom is roughly 1/5th of that on earth, gmk
The time taken by Super Mario is 2.91 seconds to reach the mystery block.
To find the time it takes for Super Mario to reach the mystery block, we can use the kinematic equation:
∆y = v0t + (1/2)at2
Where ∆y is the change in a vertical position, v0 is the initial vertical velocity, a is the acceleration due to gravity, and t is the time.
Since the mystery block is 8.2 m above Mario's head, ∆y = 8.2 m. The initial vertical velocity, v0, is 0 m/s since Mario is starting from rest. The acceleration due to gravity in the Mushroom Kingdom, gmk, is 1/5th of that on Earth, so
a = (1/5)g = (1/5)(9.8 m/s2)
a = 1.96 m/s2.
Plugging these values into the equation, we get:
8.2 m = (0 m/s)t + (1/2)(1.96 m/s2)t2
Simplifying and rearranging, we get:
t2 = (8.2 m)/(0.98 m/s2)
Taking the square root of both sides, we get:
t = √((8.2 m)/(0.98 m/s2)) = 2.91 s
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.
Calculate the fuel efficiency of a vehicle that can travel 350 km using 20l of gasoline include units in your answer
0.45-t magnetic field is perpendicular to a circular loop of wire with 53 turns and a radius of 15 cm. if the magnetic field is reduced to zero in 0.12 s, what is the magnitude of the induced emf?
The magnitude of the induced emf if magnetic field is reduced to zero in 0.12 seconds is 14.058 V.
The emf induced in a circular loop of wire is given by Faraday's law of electromagnetic induction:
emf = - N * (dΦ/dt)
where N is the number of turns in the loop,
Φ is the magnetic flux through the loop, and
(dΦ/dt) is the rate of change of magnetic flux through the loop.
The circular loop has a radius of 15 cm and consists of 53 turns of wire.
The magnetic field passing through the loop is perpendicular to its plane and has a magnitude of 0.45 T. The magnetic field is reduced to zero in 0.12 s.
The magnetic flux through the circular loop is given by:
Φ = B * A
where B is the magnetic field, and
A is the area of the circular loop.
Since the magnetic field is perpendicular to the plane of the loop, the area A is given by:
A = π * r²
where r is the radius of the circular loop.
Substituting the given values, we get:
A = π * (0.15 m)²= 0.0707 m²
Φ = B * A = (0.45 T) * (0.0707 m²) = 0.0319 Wb.
The rate of change of magnetic flux through the loop is given by:
(dΦ/dt) = -ΔΦ/Δt
where ΔΦ is the change in magnetic flux and
Δt is the time taken for the change.
Substituting the given values, we get:
(dΦ/dt) = -Φ/Δt = -(0.0319 Wb) / (0.12 s) = -0.266 Wb/s
Finally, substituting the values of N and (dΦ/dt) in Faraday's law, we get:
emf = - N * (dΦ/dt) = -(53) * (-0.266 V) = 14.058 V
Therefore, the magnitude of the induced emf in the circular loop is 14.058 V.
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What will be the final velocity of a car, if it starts to move from rest and accelerates at 10 m/s² after 5 seconds ?
Answer:
50m/s.
Explanation:
Answer:
[tex]V_f=50m/s[/tex]
Explanation:
Use the the formula for final velocity (kinematic equation):
[tex]V_f=V_i+at[/tex]
Final velocity = Initial velocity + acceleration times time
Given values:
Rest - indicates 0 initial velocity
Acceleration - 10 m/s^2
Time - 5 seconds
Insert the given values:
[tex]V_f=0+5\times10[/tex]
[tex]V_f=50m/s[/tex]
A boat float on the surface of the lake sends a signal summer force vertically down to the water the sooner trace is 0. 007 sand the speed of sound is 1,500m/s. How deep is the water?
A boat float on the surface of the lake sends a signal summer force vertically down to the water the sooner trace is 0. 007 sand the speed of sound is 1,500m/s. 21 meters deep is the water.
The time it takes for the sound wave to travel from the boat to the bottom of the lake and back is given by:
t = 2d/v
Where:
d = depth of the water
v = speed of sound in water (1,500 m/s)
We can solve for d by rearranging the equation as:
d = v × t/2
Where:
t = the time it takes for the sound wave to travel from the boat to the bottom of the lake and back, which is equal to twice the time it takes for the sound wave to travel from the boat to the bottom of the lake.
The time it takes for the sound wave to travel from the boat to the bottom of the lake is given by:
t = d/v
Where:
d = distance traveled by the sound wave (which is equal to the depth of the water)
v = speed of sound in water (1,500 m/s)
We can substitute this expression for t into the equation for d to get:
d = v × d/2v
Simplifying this expression, we get:
d/0.007 = 2 × 1500
d = 21 meters
Therefore, the depth of the water is approximately 21 meters.
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How can scientists detect a black hole if it does not emit light?
PLS HELP, ONLY 5 QUESTIONS !!!
1. Describe the troposphere. Be specific and provide details.
2. Describe the stratosphere. Be specific and provide details.
3. Describe the mesosphere. Be specific and provide details.
4. Describe the thermosphere. Be specific and provide details.
5. Describe the problems of the ozone layer and how it affects our environment.
1. The troposphere is the lowest layer of Earth's atmosphere. Most of the mass (about 75-80%) of the atmosphere is in the troposphere. Most types of clouds are found in the troposphere, and almost all weather occurs within this layer.
2. The stratosphere is very dry air and contains little water vapor. Because of this, few clouds are found in this layer and almost all clouds occur in the lower, more humid troposphere. Polar stratospheric clouds (PSCs) are the exception. PSCs appear in the lower stratosphere near the poles in winter.
3. The mesosphere lies between the thermosphere and the stratosphere. “Meso” means middle, and this is the highest layer of the atmosphere in which the gases are all mixed up rather than being layered by their mass. The mesosphere is 22 miles (35 kilometers) thick.
4. The thermosphere is a layer of Earth's atmosphere that is directly above the mesosphere and below the exosphere. It extends from about 90 km (56 miles) to between 500 and 1,000 km (311 to 621 miles) above our planet.
5. The ozone layer acts as a natural filter, absorbing most of the sun's burning ultraviolet ( UV ) rays. Stratospheric ozone depletion leads to an increase in UV -B that reach the earth's surface, where it can disrupt biological processes and damage a number of materials
Explanation: Hope This Helps!
Meadow voles are small mouse-like animals that eat plants and insects. Their niche in an ecosystem is a
A.
omnivore.
B.
herbivore.
C.
producer.
D.
scavenger.
Answer:
B. herbivore.
Explanation:
Meadow voles primarily consume plants, such as grasses, herbs, and bark, although they may also eat insects occasionally. As a result, their niche in an ecosystem is that of a herbivore, which is an organism that consumes primarily plants.
an 80 kg person weighs himself on a planet having a radius of 2500 km and finds that the scale shows 75 n.calculate the mass of planet.
The mass of the planet is approximately [tex]7.87 x 10^23 kg.[/tex]
We can use the formula for the gravitational force between two masses:
[tex]F = G * (m1 * m2) / r^2[/tex]
where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. In this case, the person's weight on the planet is equal to the force of gravity between the person and the planet: F = 75 N. The person's mass is 80 kg, so their weight on Earth would be:
[tex]W = m * g = 80 kg * 9.8 m/s^2 = 784 N[/tex]
We can set these two forces equal to each other and solve for the mass of the planet: [tex]75 N = G * (80 kg * m_planet) / (r_planet)^2\\[/tex]We can rearrange this equation to solve for the mass of the planet:
[tex]m_planet = (75 N * (2500 km)^2) / (G * 80 kg)\\[/tex]
where[tex]G = 6.674 x 10^-11 N*m^2/kg^2[/tex]is the gravitational constant.
Plugging in the values, we get: m_planet = [tex](75 N * (2500 km)^2) / (6.674 x 10^-11 N*m^2/kg^2 * 80 kg)[/tex]
m_planet = [tex]7.87 x 10^23 kg[/tex]
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Question 2
2 pts
A 76 kg person is sledding down a hill is traveling at 20 m/s when they hit a stationary 20 kg person and they end up both riding together in the
sled. How fast will they be moving together immediately after they collide?
The speed of the sled and the two people immediately after the collision is approximately 15.8 m/s.
What is the Law of conservation of momentum?The conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the sled and the two people form a closed system, because there are no external forces acting on them.
Let's define the initial state as before the collision, and the final state as after the collision. In the initial state, the sled and the 76 kg person have a momentum of:
p1 = (76 kg)(20 m/s) = 1520 kg·m/s
The second person is stationary, so their momentum is zero:
p2 = 0 kg·m/s
The total momentum before the collision is therefore:
p1i = p1 + p2 = 1520 kg·m/s + 0 kg·m/s = 1520 kg·m/s
In the final state, the two people and the sled move together with a common velocity, which we'll call v. The total mass of the system is:
m = 76 kg + 20 kg = 96 kg
The total momentum after the collision is:
p1f = m v
By the conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision:
p1i = p1f
1520 kg·m/s = 96 kg × v
Solving for v, we get:
v = 1520 kg·m/s / 96 kg ≈ 15.8 m/s
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If it takes 726 watts of power to move a mass 36 meters in 14 seconds, then what is the magnitude of the object’s mass?
A. 12. 1 kg
B. 20. 2 kg
C. 28. 8 kg
D. 282 kg
When an item must be moved 36 meters in 14 seconds using 726 watts of electricity, its mass is 28.8 kg.(c) is the right option.
Any quantity in mechanics may be defined in terms of mass, length, length time. The letter m stands for kilogram, which represents mass in the SI. Contrary to popular belief, relativistic mass must always be thought of when moving at speeds that are near to the lightest possible speed.
The Power is provided with p = 726 watt.
The Time is 14 seconds.
d = 36 m is the distance traveled.
Use the provided formula to calculate power.
p = W / t
p = m * g * h / t (w = m * g * h)
726 = m * 9.8 * 36 / 14 ( g = 10 m/s^2)
m = 28. 8kg.
As a result, the object's mass 36 m in 14 s equals 28.8 kg even when an item needs 726 watts of electricity to move it.
The mass of it as an item, a key indication of the volume of both the thing's contents, is used to calculate its inertia, a fundamental attribute. Descriptions of weight might appear circular because it's such a fundamental concept and difficult to express in words of every other concept.
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A Saturn
V
rocket's powerful boosters are capable of producing a powerful upward acceleration of
11.7 m/s 2
. During a test run of a similar rocket, NASA launches a prototype vertically upward on a calm day (no wind), burning fuel and producing a roughly constant acceleration until it reaches an upward speed of
679 m/s
. After the engines shut off, the rocket begins to freefall, eventually coming back down to the earth after reaching a maximum height of
42.3 km
. Ignoring air resistance, a) How far from the ground was the rocket when its boosters turned of and it began to freefall? b) What was the prototype rocket's upward acceleration while its boosters were firing? c) For how long were the boosters firing? d) For what total time is the rocket in the air before striking the ground?
The correct answer for a) the rocket was 19,671.65 meters (or 19.67 km) from the ground when the boosters turned off, b) rocket's upward acceleration while its boosters were firing was 11.7 m/s^2, c) the boosters were firing for 58.04 seconds, d) the rocket is in the air for a total of 199.38 seconds
a) To find the distance from the ground when the boosters turned off, we can use the formula for displacement in terms of initial velocity, acceleration, and time:
d = v_i*t + 0.5*a*t^2
We know the initial velocity (v_i) is 0 m/s, the acceleration (a) is 11.7 m/s^2, and the final velocity (v_f) is 679 m/s.
We can use the formula v_f = v_i + a*t to find the time (t) that the boosters were firing:
679 m/s = 0 m/s + 11.7 m/s^2 * t
t = 58.04 s
Now we can plug this time into the displacement formula:
d = 0 m/s * 58.04 s + 0.5 * 11.7 m/s^2 * (58.04 s)^2
d = 19,671.65 m
So the rocket was 19,671.65 meters (or 19.67 km) from the ground when the boosters turned off.
b) The prototype rocket's upward acceleration while its boosters were firing was 11.7 m/s^2, as given in the question.
c) As calculated in part a), the boosters were firing for 58.04 seconds.
d) To find the total time the rocket is in the air, we need to find the time it takes to reach its maximum height and the time it takes to fall back to the ground.
We can use the formula d = v_i*t + 0.5*a*t^2 again, with the initial velocity (v_i) being 679 m/s, the acceleration (a) being -9.8 m/s^2 (due to gravity), and the displacement (d) being the difference between the maximum height and the height when the boosters turned off:
42.3 km - 19.67 km = 22.63 km = 22,630 m
22,630 m = 679 m/s * t + 0.5 * -9.8 m/s^2 * t^2
Solving this quadratic equation gives us two solutions for t, but only one is positive:
t = 70.67 s
So the time it takes to reach the maximum height is 70.67 seconds.
The time it takes to fall back to the ground is the same, since the initial and final velocities are the same but in opposite directions. Therefore, the total time the rocket is in the air is:
t_total = 58.04 s + 70.67 s + 70.67 s = 199.38 s
So the rocket is in the air for a total of 199.38 seconds before striking the ground.
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