This is a classic case of 'velocity components.'
Imagine a vector for velocity. Now, consider that this vector could be the hypotenuse of a right triangle, with two other sides going along the x and y-axis. These sides of the triangle will have values, and adding them up using the pythagorean theorem will prove that the sum of their squares equals the square of the original vector.
Well, okay, that's nice and all, you may be saying - but how do we solve the actual question?
Let's apply this thought to the question. This vector can have both an x component and y component (essentially, parts of the vector that travel along the x and y-axis).
Now, what could these components be? We know that the stone is thrown perfectly horizontally, meaning that the x-component is quite literally the velocity.
How about the y-component? Since it's thrown at a perfect horizontal, there isn't really any vertical velocity whatsoever. There's only horizontal velocity.
"Great, fantastic! So, what's the importance of figuring out the horizontal and vertical velocities?"
When a stone is in free fall, it experiences a gravitational acceleration. This acceleration from gravity, though, only affects the vertical velocity. Since gravity is vertical as well, it's essentially impossible for the horizontal velocity to be changed at all.
This means that to solve the horizontal distance, we simply need to find the time it takes for the rock to hit the ground and multiply said time by the horizontal velocity.
Since the vertical velocity is the only thing changed by gravity, we can write out an equation that can solve for the time:
∆Y = [tex]v_{i}[/tex]t + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
We know that initial vertical velocity is zero, so:
∆Y = [tex]v_{i}[/tex]t + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
∆Y = 0t + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
∆Y = [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
We need to solve for t, so let's isolate the variable. Multiply both sides by 2 to get rid of the fraction:
∆Y * 2 = [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex] * 2
2∆Y = g[tex]t^{2}[/tex]
Divide both sides by g:
(2∆Y)/g = [tex]\frac{gt^{2} }{g}[/tex]
Square root both sides:
[tex]\sqrt{(2Y)/g}[/tex] = [tex]\sqrt{t^{2} }[/tex]
t = [tex]\sqrt{(2Y)/g}[/tex]
Input our values for Y and g (Y is the height of the cliff, and g is gravitational acceleration):
t = [tex]\sqrt{(2*50)/9.80}[/tex]
Solve:
t = [tex]\sqrt{(2*50)/9.80}[/tex]
t = 3.194 (s)
Whew! That was a lot of steps to find the time! Now that we have the time, we can find the horizontal distance the rock travels:
∆x = [tex]v_{i}[/tex]t + [tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex]
The horizontal velocity has no acceleration (gravity is vertical!), so:
∆x = [tex]v_{i}[/tex]t + [tex]\frac{1}{2}[/tex]*0*[tex]t^{2}[/tex]
∆x = [tex]v_{i}[/tex]t
The horizontal velocity is 15 m/s, and the time is 3.194:
∆x = [tex]v_{i}[/tex]t
∆x = 15 * 3.194
∆x = 47.91 (m)
Since we rounded the time, it makes sense that our final answer's a little bit off to the options. The closest one is option B, which is only 0.6m off, a tiny difference that may have come from the test maker's use of '10 m/[tex]s^{2}[/tex]' as the gravitational acceleration (while we stayed as accurate as possible with 9.80) as well as our rounding of the final time.
Option B, the stone will have travelled 47.85 meters.
If you have any questions on how I got to the answer or if you're still confused on any topic I attempted to explain, just ask in the comments and I'll try to answer it to the best of my ability! Good luck!
- breezyツ
300 grams of ethanol is heated with 14640 Joules of energy to reach a final temperature of 30 °C. What was the initial temperature of the ethanol? The specific heat of ethanol is 2.44 J/g·°C.
Answer:
10 °C
Explanation:
Applying
q = cm(t₂-t₁)............... Equation 2
Where q = heat energy, c = specific heat of ethanol, m = mass of ethanol, t₁ = initial temperature, t₂ = Final temperature.
Given: c = 2.44 J/g.°C, m = 300 g, q = 14640 J, t₂ = 30°C
Substitute into equation 2 and solve for t₁
14640 = 2.44×300(30-t₁)
14640 = 732(30-t₁)
732(30-t₁) = 14640
(30-t₁) = 14640/732
(30-t₁) = 20
t₁ = 30-20
t₁ = 10 °C
Answer:
30°C
Explanation:
i just did it
How does the Coriolis effect influence the direction of the Trade Winds in the Northern Hemisphere? Does it have the same effect in the Southern Hemisphere?
Answer:
Part A
Coriolis effect is used to describe how objects which are not fixed to the ground are deflected as they travel over long distances due to the rotation of the Earth relative to the 'linear' motion of the objects
Due to the Coriolis effect the wind flowing towards the Equator from high pressure belts in the subtropical regions in both the Northern and Southern Hemispheres are deflected towards the western direction because the Earth rotates on its axis towards the east
Part B
In the Northern Hemispheres, the winds are known as northeasterly trade winds and in the Southern Hemisphere, they are known as the southeasterly trade wind. Therefore, Coriolis effect has the same effect on the direction of the Trade Winds in the Southern Hemisphere as it does in the Northern Hemisphere
Explanation:
An astronaut drops a 1.0 kg object and a 5.0 kg object on the Moon. Both objects fall a total distance of 2.0 m vertically. Which of the following bost describes the objects after they have fallen a distance of 1.0 m2
They have each gained one-half of their maximum kinetic energy
They have cach lost the same amount of potential energy
They have each gained the same amount of potential energy
They have each lost kinetic energy
Answer:
Chupapi munyaño hoyaaaa
Refer to the image shown to answer the question.
If a light ray is reflected off the shiny surface at 170 degrees, at what angle did the light ray first strike the surface?
170 degrees
70 degrees
110 degrees
10 degrees
Answer:10
Explanation: if you look it has a 170 but some people have 70 if you have 170 then it will be 10 if you have a 70 then it will be 110 if I'm right then Yw
Answer:
10
Explanation:
i took the quiz xoxo
WILL MARK BRAINLIEST
A 75 kg cannon ball is fired from a 500 kg cannon. If the cannon balls speed is 4 m/s immediately after leaving the raft what is the recoil speed of the cannon
Answer:https://www.ux1.eiu.edu/~cfadd/1150-05/Hmwk/Ch09/Ch09.html
i has the answer that you need i think i could not take a screen shot of it sorry
Explanation:
A 1.2 kg block is held at rest against the spring with a force constant k= 730 N/m. Initially, the spring is compressed a distance d. When the block is released, it slides across a surface that is frictionless except for a rough patch of width 5.0 cm that has a coefficient of kinetic friction = 0.44. Find d, such that the block's speed after crossing the rough patch is 2.3 m/s.
Answer:
Compression distance: [tex]d \approx 0.102\,m[/tex]
Explanation:
According to this statement, we know that system is non-conservative due to the rough patch. By Principle of Energy Conservation and Work-Energy Theorem, we have the following expression that represents the system having a translational kinetic energy ([tex]K[/tex]), in joules, at the expense of elastic potential energy ([tex]U[/tex]), in joules, and overcoming work losses due to friction ([tex]W_{l}[/tex]), in joules:
[tex]K + W_{l} = U[/tex] (1)
By definitions of translational kinetic and elastic potential energies and work losses due to friction, we expand the equation described above:
[tex]\frac{1}{2}\cdot m \cdot v^{2} +\mu\cdot m\cdot g \cdot s = \frac{1}{2} \cdot k \cdot d^{2}[/tex] (2)
Where:
[tex]m[/tex] - Mass of the block, in kilograms.
[tex]v[/tex] - Final velocity of the block, in meters per second.
[tex]\mu[/tex] - KInetic coefficient of friction, no unit.
[tex]g[/tex] - Gravitational acceleration, in meters per square second.
[tex]s[/tex] - Width of the rough patch, in meters.
[tex]k[/tex] - Spring constant, in newtons per meter.
[tex]d[/tex] - Compression distance, in meters.
If we know that [tex]m = 1.2\,kg[/tex], [tex]v = 2.3\,\frac{m}{s}[/tex], [tex]\mu = 0.44[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]s = 0.05\,m[/tex] and [tex]k = 730\,\frac{N}{m}[/tex], then the compression distance of the spring is:
[tex]\frac{1}{2}\cdot m \cdot v^{2} +\mu\cdot m\cdot g \cdot s = \frac{1}{2} \cdot k \cdot d^{2}[/tex]
[tex]m\cdot v^{2} + 2\cdot m\cdot g \cdot s = k\cdot d^{2}[/tex]
[tex]d = \sqrt{\frac{m\cdot (v^{2}+2\cdot g\cdot s)}{k} }[/tex]
[tex]d \approx 0.102\,m[/tex]
What are the units of radiation?
The radiation dose absorbed by a person is measured using the conventional unit rad or the SI unit gray. The biological risk of exposure to radiation is measured using the conventional unit rem or the SI unit sievert.
I hope this helps!
Rama's weight is 4okg: She is carrying a load of 20kg up to a height of 20 meters.what work does she do?Also mention its type of work
Answer:
rama is doing
Explanation:
work done=f×d×g
=60×20×9.8
=11760j
she is doing work against gravity
mark me
A concave shaving mirror has a radius of curvature of 25.0 cm. For each of the following cases, find the magnification and determine whether the image formed is real or virtual and upright
or inverted,
(a) an upright pencil placed 46.0 cm from the mirror
(b) an upright pencil placed 5.0 cm from the mirror
(a) The magnification is less than 1, the image is smaller than the object. Therefore, the image is real, inverted, and smaller than the object. (b)The magnification is less than 1 in magnitude, the image is also smaller than the object. Therefore, the image is virtual, inverted, and smaller than the object.
What do you understand by magnification?In mirrors, magnification refers to the degree to which an object's size appears to be larger or smaller when reflected in a mirror. The magnification of a mirror is determined by its curvature and distance from the object being reflected.
We can use the mirror equation and magnification formula to solve the problem:
Mirror equation:
1/f = 1/do + 1/di
Magnification formula:
m = -di/do
where
f = focal length of the mirror
do = object distance from the mirror
di = image distance from the mirror
m = magnification
Given:
Radius of curvature, R = 25.0 cm (since the mirror is concave, R is negative)
focal length, f = R/2 = -12.5 cm
(a) For an upright pencil placed 46.0 cm from the mirror:
do = 46.0 cm
Using the mirror equation, we can solve for di:
1/f = 1/do + 1/di
1/-12.5 = 1/46.0 + 1/di
di = -17.2 cm
Since di is negative, the image is formed behind the mirror, which means it is real. Also, the magnification is:
m = -di/do = -(-17.2 cm)/46.0 cm = 0.374
Since the magnification is less than 1, the image is smaller than the object. Therefore, the image is real, inverted, and smaller than the object.
(b) For an upright pencil placed 5.0 cm from the mirror:
do = 5.0 cm
Using the mirror equation, we can solve for di:
1/f = 1/do + 1/di
1/-12.5 = 1/5.0 + 1/di
di = 3.33 cm
Since di is positive, the image is formed in front of the mirror, which means it is virtual. Also, the magnification is:
m = -di/do = -3.33 cm/5.0 cm = -0.666
Since the magnification is negative, the image is inverted. Since the magnification is less than 1 in magnitude, the image is also smaller than the object. Therefore, the image is virtual, inverted, and smaller than the object.
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How much force is needed to keep the bowling ball moving towards the pins once it has
left the man's hand?
Please help me!
Answer:
Explanation:
The amount of force needed needs to be greater than all the forces acting in the opposite direction that the bowling ball was thrown. This includes air resistance, floor friction, gravity, and any other force involved. As long as the force acting on the bowling ball that is causing it to go in the direction of the pins is slightly greater than the opposite acting forces then it will continue in that direction. Since no values are provided we cannot calculate the actual precise value of force needed.
calculate speed and velocity of the following. the race car was moving for 3.7 hours and during that time it traveled a distance of 500 miles south. what is the speed the car was travelling?
Answer:
v = 135.13 mph
Explanation:
Given that,
The race car was moving for 3.7 hours and during that time it traveled a distance of 500 miles south.
We need to find the speed of the car.
We know that,
Speed = distance/time
So,
[tex]v=\dfrac{500\ miles}{3.7\ h}\\\\v=135.13\ mph[/tex]
So, the speed of the car is equal to 135.13 mph.
A girl who is watching a plane fly tells her friend that the plane isn't moving at all. Describe a frame of reference in which the girl's description would be true.
The girl's reference frame must be moving with the same speed as the plane.
If an observer is stationary and he watches a car moving he can observe that the car has a momentum and is moving with certain speed. But if the observer is in the car or moving with same speed, the car does not appear to move away form the observer. Likewise, two observers moving with different speed will have different observation about the same car.
Similarly, if the girl describes the plane is not moving that means either she is in the plane or moving with the same speed along with the plane.
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What are the difference between copper and sodium once you put it to flame?
Answer:
When you burned the skewer tip coated with sodium chloride, you should have seen that the flame was pure yellow-orange (without any blue). This is because when the metal sodium is burned, it makes intense yellow-orange light. ... This is because when the metal copper is burned, it makes bluish-green light.
hope this helps
Please help me!! I will give brainliest!
Q: How do you determine speed over a crooked path? Explain.
Answer: If you solve for the orbit speed, v, in the mass formula, you can find how fast something needs to move to balance the inward pull of gravity: v 2 = (G M)/r . Taking the square root of both sides (you want just v not v 2), you get v = Sqrt.
Explanation:
Three resistors, 3.0 Ω, 12 Ω, and 4.0 Ω, are connected in parallel across a 6.0-V battery as shown above. What is the current through the battery?
Answer:
the current flowing through the battery is 4 A.
Explanation:
Given;
resistance of the three resistors in parallel, R₁, R₂ and R₃ = 3.0 Ω, 12 Ω, and 4.0 Ω
voltage of the battery, V = 6.0 V
The equivalent resistance is calculated as follows;
[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \\\\\frac{1}{R_T} = \frac{1}{3} + \frac{1}{12} + \frac{1}{4} \\\\\frac{1}{R_T} = \frac{4 \ + \ 1 \ + \ 3}{12} \\\\\frac{1}{R_T} = \frac{8}{12} \\\\\frac{1}{R_T} = \frac{2}{3} \\\\R_T = \frac{3}{2} \\\\R_T = 1.5 \ ohms[/tex]
The current flowing through the battery is calculated as follows;
[tex]I = \frac{V}{R_T} \\\\I = \frac{6}{1.5} \\\\I = 4 \ A[/tex]
Therefore, the current flowing through the battery is 4 A.
Uranium-238 undergoes alpha decay. In addition to the alpha particle, which isotope forms?
Answer: B - 234/90 TH
Explanation: A P 3 X
Answer: B - 234/90 TH
Explanation:
Kara started a new exercise program. Kara’s sister works out with her on a regular basis and even talks to Kara about her progress. In this scenario, what is another name for Kara’s sister?
A.
goal-setter
B.
self-monitor
C.
support system
D.
nutritionist
A spring oscillates with a period of
0.228 S. What is its frequency?
(Unit = Hz)
Answer:4.39
Explanation:For acellus students the answer is 4.39
the velocity of a car changes from 20 m/s east to 5 m/s east in 5 seconds. What is the acceleration of the car?
Answer:
3 m/s²
Explanation:
Acceleration = Change in velocity/ time
= (20 - 5) / 5
= 3 m/s²
What is the solution to unit for measuring electric current?
Answer:
The SI unit for electric current is Ampere (A)
What is the unit for efficiency?
What is the biggest number the
efficiency can be?
How do you work out the % efficiency?
Answer:
Efficiency has no physical units (example .85 = 85%)
The largest number would be 1 or 100%
An example of efficiency is: work out/work in
or (work in - work lost to friction) / work in would be an example of the efficiency of the process
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“a car is parked uphill on a sloped street. How would you draw the force diagram to illustrate all of the forces acting on this car to keep it parked on the slope?”
Answer:
Explanation:
There are 3 main forces at work here, gravity, normal and friction. The gravity pulls the car straight down and is what keeps the car on the ground. Normal force is straight up from the points where the car is touching, so since the wheels are the only parts of the car touching the street, this is where all the normal force is. Friction force opposes any and all motion, the car wants to slide down the hill and would slide down the hill if there was no friction, so the friction force is in the opposite direction of the cars intended motion.
At the depth of 10 m, the diver breathes in air from the scuba tank, filling her lungs with air whose pressure equals that of the surrounding water. How does the number of air molecules in her lungs compare with the number she had in a full breath at the surface?
A. Half as many
B. The same
C. Twice as many
D. Four times as many
Answer:
The number of air molecules in her lung compared with the number she had in a full breadth at the surface is;
C. Twice as many
Explanation:
The depth at which the scuba diver fills her lungs with air, d = 10 m
Pressure of fluid = Density, ρ × Acceleration due to gravity, 'g' × Depth, 'd'
Where;
ρ = 970 kg/m³
g ≈ 9.81 m/s²
∴ The pressure of the water of the 10 m water column = 970 kg/m³ × 9.81 m/s² × 10 m = 95,157 Pa
The atmospheric pressure, P₁ = 101,325 Pa
The total pressure at the 10 m depth = The atmospheric pressure + The pressure of the water of the 10 m water column
∴ The total pressure at the 10 m depth, P₂ = 95,157 Pa + 101,325 Pa = 196,482 Pa
By the combined gas law, we have;
P₁·V₁/n₁ = P₂·V₂/n₂
Where;
P₁ = The atmospheric pressure
P₂ = The pressure at 10 m depth
V₁ = V₂ = The volume of her lungs
n₁ = The number of air molecules at the surface that fills her lungs
n₂ = The number of air molecules that fills her lungs at the 10 m depth
Therefore, we have;
P₂/P₁ = n₂/n₁ × V₁/V₂
From V₁ = V₂, we have;
P₂/P₁ = n₂/n₁ × V₁/V₁ = n₂/n₁ × 1
∴ P₂/P₁ = n₂/n₁
P₂/P₁ = 196,482/101,325 ≈ 2
∴ P₂/P₁ = n₂/n₁ ≈ 2
n₂ ≈ 2 × n₁
The number of air molecules that fills her lungs at the 10 m depth, n₂ is approximately 2 times (twice) as many as the number of air molecules at the surface that fills her lungs, n₁
Therefore the correct option is twice as many molecules as she had in a full breath at the surface is required to fill her lungs at the 10 m water depth.
This question involves the concepts of pressure, the equation of state, and the number of molecules.
The number of molecules in hr breathe are "C. twice as many" as compared to the number of molecules in her lungs when she had a full breath at the surface.
According to the equation of state:
[tex]\frac{P_1V_1}{n_1}=\frac{P_2V_2}{n_2}[/tex]
where,
n₁ = no. of molecules in lungs at surface
n₂ = no. of molecules in lungs at depth
P₁ = Pressure at surface = Atmospheric Pressure = 101325 Pa
P₂ = Pressure at depth = 101325 Pa + ρgh
P₂ = 101325 Pa + (1000 kg/m³)(9.81 m/s²)(10 m) = 199425 Pa
V₁ = V₂ = V = Volume of lungs
Therefore,
[tex]\frac{(101325\ Pa)V}{n_1}=\frac{(199425\ Pa)V}{n_2}\\\\[/tex]
n₂ = 2 n₁
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How can you cause a substance to turn from a solid to a liquid or from a liquid to a gas? Help
Answer:
When the temperature increases
Explanation:
Which of the following factors should be considered when designing a personal fitness program?
A goals
В. activities
C. variety
D. all of the above
A projectile thrown up ward moves in its parabolic path at what point..
Answer:
please give me brainlist and follow
Explanation:
As the projectile moves upward, its vertical component of velocity decreases due to gravity. While the horizontal component remains the same as there is no acceleration in the horizontal direction. At maximum height vertical component of velocity is zero.
Ignoring air resistance, an object thrown in any direction moves in a parabolic path from the time it leaves the thrower's hand until the time it hits the ground or a physical obstruction.
Which would have more volume, 1 kg of lead or 1 kg of copper? And EXPLAIN how you can tell.
Pls answer this ASAP for 15 points
What are the first three harmonics of a note produced on a 0.31 m long violin string if the waves on this string have a speed of 274.4 M/s
Answer:
442 Hz, 882 Hz, 1330 Hz
Explanation:
Given data: length of the string= 0.31 m = 31 cm
speed of the waves = 274.4 M/s or 2740 cm/s
Wavelengths are
62 cm
31 cm and
62 / 3 = 20.67 cm
The frequencies associated with these wavelengths ( which are the 1st, 2nd and 3rd harmonics )
are
27440/ 62 = 442.6 = 442 Hz
27440/31 = 885.2 = 882 Hz
27440 / 20.67 = 1328 = 1330 Hz
Oxygen Supply in Submarines Nuclear submarines can stay under water nearly indefinitely because they can produce their own oxygen by electrolysis of water.
How many liters of O2 at 298 K and 1.00 bar are produced in 1.00 hr in an electrolytic cell operating at a current of 0.0200 A?
Answer:
1.865 * 10^-4 L
Explanation:
The equation of the reaction is:
4OH^-(aq) ----->2H2O(l) + O2(g) + 4e
Since one mole of oxygen which occupies 22.4 L is produced in the electrolysis of water by 4 Faraday of electricity as shown in the equation above;
Then;
4 * 96500 C liberates 22.4 L of oxygen
60 * 60 * 0.0200 C will liberate 60 * 60 * 0.0200 * 22.4/4 * 96500
= 1.865 * 10^-4 L
If the needle in the galvanometer is going up, what can you conclude about the motion of the magnet in the diagram?
It is not moving.
It must be moving left.
It must be moving right.
It is being moved in an unknown direction.
If the needle in the galvanometer is going up, the conclusion about the motion of the magnet is it must be moving right.
What is galvanometer?The galvanometer is the device used to detect the small current when moving coil is deflected.
When the magnet is moved towards or into the coil of wire, the magnetic field will change and voltage will be generated into the coil. The coil must be moving to the right when galvanometer going up.
Thus, the conclusion about the motion of the magnet is, it must be moving to the right.
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