Answer:
a) 2nd case rate of rotation gives the greater speed for the ball
b) 1534.98 m/s^2
c) 1515.04 m/s^2
Explanation:
(a) v = ωR
when R = 0.60, ω = 8.05×2π
v = 0.60×8.05×2π = 30.34 m/s
Now in 2nd case
when R = 0.90, ω = 6.53×2π
v = 0.90×6.53×2π = 36.92 m/s
6.35 rev/s gives greater speed for the ball.
(b) a = ω^2 R = (8.05×2π)^2 )(0.60) = 1534.98 m/s^2
(c) a = ω^2 R = (6.53×2π)^2 )(0.90) = 1515.05 m/s^2
If two radio telescope dishes are wired together in the right way, the "D" used in determining the angular resolution is determined by
Answer:
D is determined by distance between the telescopes.
Explanation:
A spherical balloon contains a charge +Q uniformly distributed over its surface. When it has a diameter D, the electric field at its surface has magnitude E. If the balloon is not blown up to thrice this diameter without changing the charge, the electric field at its surface is?
Answer:
E = 1/9 E₀
Explanation:
In this exercise we are told that the electric field is Eo when the diameter of the balloon is D, the expression
we are asked to shorten the electric field when the diameter is 3D with the same eclectic charge
For this we can use the gauss law to find the field in the new diameter, for this we create a Gaussian surface in the form of a sphere
Ф = ∫ E. dA = [tex]q_{int}[/tex] /ε₀
In this case the lines of the electric field and the radii of the sphere are parallel, therefore the scalar product is reduced to the algebraic product and the charge inside the sphere is the initial charge Q
A = 4π r²
E 4π r² = Q /ε₀
E = 1 /4πε₀ Q / r²
the value of the indicated distance is 3 times the initial diamete
r = 3 D / 2
we substitute
E = 1/4 πε₀ Q (2/ 3D)²
for the initial conditions
E₀ = 1 / 4πε₀ Q (2/D)²
subtitled in the equation above
E = 1/9 E₀
Parallel rays of monochromatic light with wavelength 583 nm illuminate two identical slits and produce an interference pattern on a screen that is 75.0 cm from the slits. The centers of the slits are 0.640 mm apart and the width of each slit is 0.434 mm. If the intensity at the center of the central maximum is 5.00×10^−4W/m^2. What is the intensity at a point on the screen that is 0.900 mm from the center of the central maximum?
Answer:
I = 2.18 10⁻⁴ W / m²
Explanation:
The two-slit interference pattern is described by the expression for constructive interference.
d sin θ = m λ
If we also want to know the distribution of intensities we must perform the su of the electric field of the two waves, and find the intensity as the square of the velvet field, obtaining the expression
I = I_max cos² ((π d /λ L) y)
where d is the separation of the slits, λ the wavelength, L the distance to the screen e and the separation of the interference line with respect to the central maximum
let's reduce the magnitudes to the SI system
λ = 583 nm = 583 10⁻⁹ m
L = 75.0 cm = 75.0 10⁻² m
d = 0.640 mm = 0.640 10⁻³ m
y = 0.900 mm = 0.900 10⁻³ m
let's calculate the intensity of this line
I = 5 10⁻⁴ cos² ((π 0.640 10⁻³ /583 10⁻⁹ 0.75 10⁻²) 0.900 10⁻³)
I = 5 10⁻⁴ cos2 (413.84)
I = 5 10⁻⁴ 0.435
I = 2.18 10⁻⁴ W / m²
Zuckerman’s test for sensation seeking measures which of the following characteristics?
dangerousness, antisocial traits, “letting loose,’ and intolerance for boredom
thrill and adventure seeking, experience seeking, disinhibition, and susceptibility to boredom
adventurousness, physical prowess, creative morality, and charisma
dangerousness, adventurousness, creativity, and thrill and adventure seeking
The correct answer is B. thrill and adventure seeking, experience seeking, disinhibition, and susceptibility to boredom
Explanation:
Marvin Zuckerman was an important American Psychologists mainly known for his research about personality and the creation of a model to study this aspect of human psychology. This model purposes five factors define personality, these are the thrill and adventure-seeking that involves seeking for adventures and danger; experience seeking that implies a strong interest in participating in new activities; disinhibition that implies being open and extrovert; and susceptibility to boredom that implies avoiding boredom or repetition. Thus, option B correctly describes the characteristics used in Zuckerman's test.
Air bags greatly reduces the chance of injury in a car accident.explain how they do so in terms of energy transfer
Answer:
Airbags reduce chances of injury by absorbing most of the impact force from the body during a car crash
Explanation:
In a car collision, the speed of the vehicle is suddenly bought to rest. All the kinetic energy is suddenly converted into other forms of energy.
The body of the driver keeps travelling forward under his inertia force due to his mass until he is slammed against the steering wheel. The steering wheel is a very rigid component, and so when the body slams against it, the body takes the deformation, absorbing some of the energy of the moving car. This sudden impact of energy can be fatal enough to gravely injure the driver because the body does not undergo much deformation. When an airbag is used, the crash automatically triggers the release of the airbag. Instead of the body colliding against the rigid steering wheel, it is now collided against the soft air bag. The airbag is very collapsible, and some of the kinetic energy of the car on the driver is converted into the deformation energy used to deform the airbag when they collide. In the process of deformation, the time of impact is extended, reducing the force impacted on the driver, reducing the fatality of the impact.
A car has a mass of 1200 kg and an acceleration of 4 m/s^2. If the friction on the car is 200 N, how much force is the thrust providing?
Answer:
5000N
Explanation:
According to Newton's second law of motion, the net force (∑F) acting on a body is the product of the mass (m) of the body and the acceleration (a) of the body caused by the force. i.e
∑F = m x a -------------(i)
From the question, the net force is the combined effect of the thrust (F) and the friction force (Fₓ). i.e
∑F = F + Fₓ -------------(ii)
Where;
Fₓ = -200N [negative sign because the friction force opposes motion]
Combine equations(i) and (ii) together to get;
F + Fₓ = m x a
F = ma - Fₓ -------------(iii)
Where;
m = mass of car = 1200kg
a = acceleration of the car = 4m/s²
Now substitute the values of m, a and Fₓ into equation (iii) as follows;
F = (1200 x 4) - (-200)
F = 4800 + 200
F = 5000N
Therefore, the force the thrust is providing is 5000N
A neutral metal ball is suspended by a string. A positively charged insulating rod is placed near the ball, which is observed to be attracted to the rod. This is because:____________.
a. the ball becomes negatively charged by induction
b. the ball becomes positively charged by induction
c. the string is not a perfect insulator
d. there is a rearrangement of the electrons in the ball
e. the number of electrons in the ball is more than the number in the rod
Answer:
d. there is a rearrangement of the electrons in the ball
Explanation:
Inside the neutral metal ball, there are equal no. of positive charges (protons) and negative charges (electrons). Normally, the charges are distributed evenly throughout the ball.
However, when the positively charged insulating rod is brought near, since positive charges and negative charges attract each other, the electrons (-ve charges) in the metal ball moves towards the side nearest to the rod. The metal ball gets attracted to the rod.
a and b are not correct because the rod is insulating, so electrons cannot be transferred between them to induce a net charge in the metal ball. the no. of electrons is unrelated to the attraction between opposite charges , so e is incorrect as well.
In which case is the speed of laser light the slowest relative to the observer? a person walking in the street and who sees laser light emitted from a low‑speed car that moves in the same direction as the person a student sitting in the classroom and who see laser light from the pointer used by the instructor laser light emitted from a high‑speed aircraft and detected by another high‑speed aircraft traveling in the opposite direction a person who sees laser light passing through a bucket full of water it is the same for all of the above
Answer:
a person who sees laser light passing through a bucket full of water.
Explanation:
According to relativity, the speed of light is the same irrespective of the relative speed between the source, and the observer. The only exception is when light travel from a less dense medium to a denser medium as in air into the bucket full of water. So the speed of light is slowest relative to the observer in the laser that passes through the bucket of water.
How many components do vectors have, and what are they?
Answer:
There are two components for a two-dimensional coordinate system/vector.
Explanation:
For two-dimensional vectors, such as velocity, acceleraton, etc, there are two components, the x- and y-components.
These components could be rotated or translated, depending on the coordinate system.
Instead of rectangular cartesian system, the components could also be in the form of polar coordinates, such as radius and theta (angle).
For three-dimensional vectors, such as velocity in space, there are three components, in various coordinate systems.
The only factor connecting horizontal and vertical components of projectile motion is _____.
Answer:
VelocityExplanation:
When a body is launched in air and allowed to fall freely under the influence of gravity, the motion experienced by the body is known as a projectile motion. The body is launched at a particular velocity and at an angle theta to the horizontal. The velocity of the body ca be resolved towards the horizontal component and the vertical component.
Along the horizontal Ux = Ucos(theta)
Along the vertical Uy = Ucos(theta)
Ux and Uy are the velocities of the body along the horizontal and vertical components respectively.
This means that the only factor connecting horizontal and vertical components of projectile motion is its velocity since we are able to calculate the velocity of the body along both components irrespective of its initial velocity.
If a capacitor is being charged by 1.0 A of current flowing onto its plates, the displacement current between the plates will be
Answer is given below
Explanation:
When current occurs due to charge flow, it is called conduction. Since there are no conductors between the plates of the capacitor, there is no charge transfer between them and the conduction current becomes zero. However, when the capacitor is charged, the charges accumulate on the plates and, therefore, the electric field across the plates E increases with time. This variation of the electric field in the plates of the capacitor is called the displacement current, so in the displacement current, there is no electric current due to the movement of the charges, but due to the variation of the electric field between the two points.so I ∝ Rate of accumulations of the charge across plate capacitorI = [tex]\frac{dQ}{dt}[/tex] I = i (cond)I = 1 AA motorcyclist changes his speed from 20 km / h to 100 km / h in 3 seconds, maintaining a constant acceleration in that time interval. If the mass of the motorcycle is 200 kg and that of its rider is 80 kg, what is the value of the net force to accelerate the motorcycle? Help!
Answer:
2000 N
Explanation:
20 km/h = 5.56 m/s
100 km/h = 27.78 m/s
F = ma
F = m Δv/Δt
F = (200 kg + 80 kg) (27.78 m/s − 5.56 m/s) / (3 s)
F = 2074 N
Rounded to one significant figure, the force is 2000 N.
A 11-cm-long spring is attached to the ceiling. When a 2.4kg mass is hung from it, the spring stretches to a length of 18cm .
Part A What is the spring constant k?
Part B How long is the spring when a 3.0 kg mass is suspended from it?
Answer:
Part A : 336 N/m
Part B: 19.75 cm
Explanation:
Part A: Using hooks law,
F = ke................... Equation 1
Where F = Force applied to the spring, k = spring constant, e = extension.
Note: From the question, the force applied to the spring is the weight of the mass hung on it.
Hence,
F = mg............... Equation 2
Substitute equation 2 into equation 1.
mg = ke
make k the subject of the equation
k = mg/e.............. Equation 3
Given: m = 2.4 kg, e = 18-11 = 7 cm = 0.07 m
Constant: g = 9.8 m/s²
Substitute these value into equation 3
k = 2.4(9.8)/(0.07)
k = 336 N/m.
Part B,
Similarly,
mg = ke.
make e the subject of the equation
e = mg/k................ Equation 4
Given: m = 3.0 kg, k = 336 N/m, g = 9.8 m/s²
Substitute into equation 4
e = 3.0(9.8)/336
e = 0.0875 m
e = 8.75 cm
Length of the spring = original length+ extension
Length of the spring = 11+8.75
Length of the spring = 19.75 cm.
While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 52-kg person develops a power of 80 W during a race, how fast is the person running
Answer:
The person is running at a speed of 2.564 m/s
Explanation:
Given;
mechanical energy dissipated per kilogram per step, E/kg/S = 0.6 J/kg/S
mass of the person, m = 52 kg
power developed by the person, P = 80 W
mechanical energy of the person per step, E = 0.6 J/kg x 52 kg
[tex]E_{step}[/tex] = 31.2 J
mechanical energy for the total step, [tex]E_{total}[/tex] = 31.2 J x S
P = E / t
[tex]P_{avg} = \frac{E_{total}}{t} \\\\P_{avg} = \frac{E_{step}*S}{t}\\\\\frac{P_{avg}}{E_{step}} = \frac{S}{t} \\\\\frac{S}{t} = \frac{80}{31.2} \\\\\frac{S}{t} = 2.564 \ m/s[/tex]
Therefore, the person is running at a speed of 2.564 m/s
To maintain the same amount of torque due to a mass on a balance as the mass is increased, how should the position of the mass change
Answer:
the mass should be bring closer to the point about which we are finding torque
Explanation:
τ = Σr × F = rmg
where m is the mass, g is acceleration due to gravity, and r is the distance
Torque is directly proportional to -
1.mass, m , of object
2. distance, r, of the mass from the point about which we are finding the torque.
So if we increase or decrease them then the torque will also increase or decrease.
So if we increase the mass the torque will increase but since we have to maintain same torque therefore we have to decrease the distance of mass from the point about which we are finding torque.
Therefore the mass should be bring closer to the point about which we are finding torque.
A flare is dropped from an airplane flying horizontally at uniform velocity (constant speed in a straight line). Neglecting air resistance, the flare will:_______. A) quickly lag behind the plane B) remain vertically under the plane C) move ahead of the plane explain
Answer:
Option B (remain vertically under the plane) is the correct option.
Explanation:
A flare would follow a particle trajectory with horizontal direction somewhat like airplane velocity as well as initial maximum motion as null but instead, gravity will induce acceleration. It would be lowered vertically underneath the plane before flare had already sunk to something like the surface.There is no different movement in the airplane nor even the flash. And none of them can change its horizontal level.Some other alternatives are given really aren't linked to the specified scenario. So choice B is the perfect solution to that.
A wave is described by the equation y(x, t) = 35 sin (2 π x - 3 t +1.5), where all numerical values and variables have the appropriate units to produce displacement in cm, speed in cm/s, and time in seconds. What is the speed of the wave?
Answer:
v = 0.477m/s
Explanation:
You have the following wave function:
[tex]y(x,t)=35sin(2\pix-3t+1.5)[/tex] (1)
where y is the vertical displacement of the wave for the position x.
The general form of a wave function can be written as follow:
[tex]y(x,t)=Asin(kx-\omega t+\phi)[/tex] (2)
by comparing the equation (2) and (1) you have:
A: amplitude of the wave = 35
k: wave number = 2π
w: angular frequency of the wave = 3
φ: phase of the wave = 1.5
The speed of the wave is given by the following formula:
[tex]v=\frac{\omega}{k}[/tex]
you replace the values of the parameters in the previous formula:
[tex]v=\frac{3}{2\pi}=0.477\frac{m}{s}[/tex]
The speed of the wave is 0.477m/s
A 25-kilogram object is placed on a compression spring, and it creates a displacement of 0.15 meters. What is the weight of an object that creates a displacement of 0.23 m on the same spring? Enter your answer as a number rounded to the nearest tenth, such as: 42.5
Answer:
I hope it is correct ✌️
A wave traveling in a string in the positive x direction has a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2 s. What is the wave equation (in base SI units) that correctly describes this wave
Explanation:
It is given that,
Wavelength of a wave, [tex]\lambda=35\ cm=0.35\ m[/tex]
Amplitude, [tex]A=8.4\ cm[/tex]
Period of the wavelength, t = 1.2 s
The wave is traveling in a string in the positive x direction. We need to write the wave equation for this conditions.
The general equation of the wave when it is traveling in +x direction is given by :
[tex]y=A\sin(kx-\omega t)[/tex]
A is amplitude
k is propagation constant
[tex]k=\dfrac{2\pi}{\lambda}\\\\k=\dfrac{2\pi}{0.35}\\\\k=17.95\ m^{-1}\approx 18\ m^{-1}[/tex]
[tex]\omega[/tex] is angular frequency
[tex]\omega=\dfrac{2\pi}{T}\\\\\omega=\dfrac{2\pi}{1.2}\\\\\omega=5.23\ s^{-1}[/tex]
So, the wave equation is given by :
[tex]y(x,t)=(0.084) \sin (18 x - 5.2 t)[/tex]
Hence, this is the required solution.
Inside a 30.2 cm internal diameter stainless steel pan on a gas stove water is being boiled at 1 atm pressure. If the water level in the pan drops by 1.45 cm in 18.6 min, determine the rate of heat transfer to the pan in watts. (Give your answer in 3 significant digits.)
Answer:
Q = 20.22 x 10³ W = 20.22 KW
Explanation:
First we need to find the volume of water dropped.
Volume = V = πr²h
where,
r = radius of pan = 30.2 cm/2 = 15.1 cm = 0.151 m
h = height drop = 1.45 cm = 0.0145 m
Therefore,
V = π(0.151 m)²(0.0145 m)
V = 1.038 x 10⁻³ m³
Now, we find the mass of the water that is vaporized.
m = ρV
where,
m = mass = ?
ρ = density of water = 1000 kg/m³
Therefore,
m = (1000 kg/m³)(1.038 x 10⁻³ m³)
m = 1.038 kg
Now, we calculate the heat required to vaporize this amount of water.
q = mH
where,
H = Heat of vaporization of water = 22.6 x 10⁵ J/kg
Therefore,
q = (1.038 kg)(22.6 x 10⁵ J/kg)
q = 23.46 x 10⁵ J
Now, for the rate of heat transfer:
Rate of Heat Transfer = Q = q/t
where,
t = time = (18.6 min)(60 s/1 min) = 1116 s
Therefore,
Q = (23.46 x 10⁵ J)/1116 s
Q = 20.22 x 10³ W = 20.22 KW
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12 + 35 t + 1
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12t² + 35 t + 1
Answer:
Velocity = 131 m/s
Speed = 131 m/s
Explanation:
Equation of motion, s = f(t) = 12t² + 35 t + 1
To get velocity of the particle, let us find the first derivative of s
v (t) = ds/dt = 24t + 35
At t = 4
v(4) = 24(4) + 35
v(4) = 131 m/s
Speed is the magnitude of velocity. Since the velocity is already positive, speed is also 131 m/s
You prepare tea with 0.250 kg of water at 85.0 ºC and let it cool down to room temperature (20.0 ºC) before drinking it. Essentially, the cooling process is isothermal to the air in your kitchen. Calculate the entropy change of the air as the tea cools, assuming that all the heat lost by the water goes into the air
Answer:
232 J/K
Explanation:
The amount of heat gained by the air = the amount of heat lost by the tea.
q_air = -q_tea
q = -mCΔT
q = -(0.250 kg) (4184 J/kg/ºC) (20.0ºC − 85.0ºC)
q = 68,000 J
The change in entropy is:
dS = dQ/T
Since the room temperature is constant (isothermal):
ΔS = ΔQ/T
Plug in values (remember to use absolute temperature):
ΔS = (68,000 J) / (293 K)
ΔS = 232 J/K
A futuristic design for a car is to have a large disklike flywheel within the car storing kinetic energy. The flywheel has mass 370 kg with a radius of 0.50 m and can rotate up to 540 rev/s. Assuming all of this stored kinetic energy could be transferred to the linear velocity of the 1600 kg car, find the maximum attainable speed of the car.
Answer:
Explanation:
Rotational kinetic energy of flywheel
= 1/2 Iω² where I is moment of inertia , ω is angular velocity
for wheel I = 1/2 m R² where m is mass and R is radius of flywheel
Putting the values
I = 1/2 x 370 x .5²
= 46.25 kg m²
ω = 2πn where n is frequency of revolution per second
ω = 2 x 3.14 x 540 = 3391.2
Rotational kinetic energy = .5 x 46.25 x 3391.2²
= 265.94 x 10⁶ J
If this energy is transferred to a car of mass 1600kg , velocity acquired by it be v , then
kinetic energy of car = rotational kinetic energy of flywheel
= 1/2 m v ² = 265.94 x 10⁶
.5 x 1600 v² = 265.94 x 10⁶
v² = 33.24 x 10⁴
v = 5.76 x 10²
= 576 m /s
Use the slider to apply a force of about 400 N. After 2 s have elapsed in the simulation, decrease the Applied Force (force exerted) slowly back to zero. Try to do this adjustment in roughly 2 s . While the Applied Force (force exerted) is decreasing, the velocity is:______.
a. constant.
b. increasing.
c. decreasing.
Answer:
c. decreasing.
Explanation:
Force produces acceleration or deceleration. Force is the product of a body's mass and its acceleration. When a force is applied to an object, the force tends to cause the body to move if the body was originally stagnant, cause the body to accelerate if applied in the direction of the body's velocity, or decelerate the body if applied in opposite direction to the velocity of the body. When the force that is exerted on a moving body is slowly reduced to zero, frictional forces between the body and the floor surface gradually decelerates the body. When this deceleration occurs, the velocity of the body gradually decreases t a stop.
based on the periodic table, which element is the best electrical conductor
Answer:
its a magnesium because it only metal in option and metals are capable to conduct electricity.
Answer:
Magnesium (Mg)
Explanation:
According to the periodic table, Metals have a high electrical conductivity than non-metals. Magnesium is a metal so it has a high electrical conductivity. Rest of them (Cl, Ne, and O ) are non-metals.
Think about a time you heard a sound come from another room in your house. How did those sound waves get to you if there were obstacles like walls in the way?
Answer:
this sound wave get to the other by either undergoing either reflection,absorption or transmission
Explanation:
When a sound wave meets an obstacle, some of the sound is reflected back from the front surface and some of the sound passes into the obstacle material, where it is absorbed or transmitted through the material like the building walls
Thus, Reflection and absorption are dependent on the wavelength of the sound. Hence percentage of the sound transmitted through an obstacle depends on how much sound is reflected and how much is absorbed.
Two parallel plates 0.800 cm apart are equally and oppositely charged. An electron is released from rest at the surface of the negative plate and simultaneously a proton is released from rest at the surface of the positive plate.
How far from the negative plate is the point at which the electron and proton pass each other?
Express your answer with the appropriate units.
Answer:
0.79 cm
Explanation:
The computation is shown below:-
Particle acceleration is
[tex]a = \frac{qE}{m}[/tex]
We will take d which indicates distance as from the negative plate, so the travel by proton is 0.800 cm - d at the same time
[tex]d = \frac{1}{2} a_et^2\\\\0.800 cm - d = \frac{1}{2} a_pt^2\\\\\frac{d}{0.800 cm - d} = \frac{a_e}{a_p} \\\\\frac{d}{0.800 cm - d} = \frac{m_p}{m_e} \\\\\frac{d}{0.800 cm - d} = \frac{1836m_e}{m_e}[/tex]
After solving the equation we will get 0.79 cm from the negative plate.
Therefore it is 0.79 cm far from the negative pate i.e the point at which the electron and proton pass each other
The point at which the electron and proton pass each other will be 0.79 cm.
What is the charge?When the matter is put in an electromagnetic field, it has an electric charge, which causes it to experience a force. A positive or negative electric charge can exist.
The given data in the problem is;
d' is the distance between the two parallel plates= 0.800 cm
The acceleration is given as;
[tex]\rm a= \frac{qE}{m} \\\\[/tex]
The distance from Newton's law is found as;
[tex]d = ut+\frac{1}{2} at^2 \\\\ u=0 \\\\ d= \frac{1}{2} at^2 \\\\ d-d' = \frac{1}{2} a_pt^2 \\\\ 0.800-d= \frac{1}{2} a_pt^2 \\\\\ \frac{d}{0.800-d} =\frac{a}{a_p} \\\\ \frac{d}{0.800-d} =\frac{m_p}{m} \\\\ \frac{d}{0.800-d} =\frac{1836m_e}{m_e} \\\\ d=0.79 \ cm[/tex]
Hence the point at which the electron and proton pass each other will be 0.79 cm.
To learn more about the charge refer to the link;
https://brainly.com/question/24391667
Taking force , length and time as fundamental quantity , find the dimensional formula for density
Answer:
fundamental formula for density = Kg/m³
Explanation:
density = mass/volume
A hungry 177 kg lion running northward at 81.8 km/hr attacks and holds onto a 32.0 kg Thomson's gazelle running eastward at 59.0 km/hr. Find the final speed of the lion–gazelle system immediately after the attack.
Answer:
The final speed of the lion-gazelle system immediately after the attack is 69.862 kilometers per hour.
Explanation:
Let suppose that lion and Thomson's gazelle are running at constant speed before and after collision and that collision is entirely inelastic. Given the absence of external force, the Principle of Momentum Conservation is applied such that:
[tex]\vec p_{L} + \vec p_{G} = \vec p_{F}[/tex]
Where:
[tex]\vec p_{L}[/tex] - Linear momentum of the lion, measured in kilograms-meters per second.
[tex]\vec p_{G}[/tex] - Linear momentum of the Thomson's gazelle, measured in kilograms-meters per second.
[tex]\vec p_{F}[/tex] - Linear momentum of the lion-Thomson's gazelle, measured in kilograms-meters per second.
After using the definition of momentum, the system is expanded:
[tex]m_{L}\cdot \vec v_{L} + m_{G}\cdot \vec v_{G} = (m_{L} + m_{G})\cdot \vec v_{F}[/tex]
Vectorially speaking, the final velocity of the lion-gazelle system is:
[tex]\vec v_{F} = \frac{m_{L}}{m_{L}+m_{G}}\cdot \vec v_{L} + \frac{m_{G}}{m_{L}+m_{G}}\cdot \vec v_{G}[/tex]
Where:
[tex]m_{L}[/tex], [tex]m_{G}[/tex] - Masses of the lion and the Thomson's gazelle, respectively. Measured in kilograms.
[tex]\vec v_{L}[/tex], [tex]\vec v_{G}[/tex], [tex]\vec v_{F}[/tex] - Velocities of the lion, Thomson's gazelle and the lion-gazelle system. respectively. Measured in meters per second.
If [tex]m_{L} = 177\,kg[/tex], [tex]m_{G} = 32\,kg[/tex], [tex]\vec v_{L} = 81.8\cdot j\,\left[\frac{km}{h} \right][/tex] and [tex]\vec v_{G} = 59.0\cdot i\,\left[\frac{km}{h} \right][/tex], the final velocity of the lion-gazelle system is:
[tex]\vec v_{F} = \frac{177\,kg}{177\,kg+32\,kg}\cdot \left(81.8\cdot j\right)\,\left[\frac{km}{h} \right] + \frac{32\,kg}{177\,kg+32\,kg}\cdot \left(59.0\cdot i\right)\,\left[\frac{km}{h} \right][/tex]
[tex]\vec v_{F} = 9.033\cdot i + 69.276\cdot j\,\left[\frac{km}{h} \right][/tex]
The speed of the system is the magnitude of the velocity vector, which can be found by means of the Pythagorean theorem:
[tex]\|\vec v_{F}\| = \sqrt{\left(9.033\frac{km}{h} \right)^{2}+\left(69.276\frac{km}{h} \right)^{2}}[/tex]
[tex]\|\vec v_{F}\| \approx 69.862\,\frac{km}{h}[/tex]
The final speed of the lion-gazelle system immediately after the attack is 69.862 kilometers per hour.
B. A car moving at an initial speed vi applies its brakes and skids for some distance until coming to a complete stop. If the coefficient of kinetic friction between tires and the road is µk what distance did the car skid?
Complete Question
The complete question is shown on the first uploaded image
Answer:
The distance which the car skid is [tex]l = \frac{v_i^2 }{2 * \mu_k * g }[/tex]
Explanation:
From the question we are told that
The initial velocity of the car is [tex]v_i[/tex]
The coefficient of kinetic friction is [tex]\mu_k[/tex]
According to the law of energy conservation
The initial Mechanical Energy = The final Mechanical Energy
[tex]M_i = M_f[/tex]
The initial mechanical energy is mathematically represented as
[tex]M_i = KE _o + PE_e[/tex]
where KE is the initial kinetic energy which is mathematically represented as
[tex]KE = \frac{1}{2} m v_i^2[/tex]
And PE is the initial potential energy which is zero given that the car is on the ground
Now
[tex]M_f = W_{\mu}[/tex]
Where [tex]W_{\mu}[/tex] is the work which friction exerted on the car which is mathematically represented as
[tex]W_{\mu} = m* \mu_k * g * l[/tex]
Where [tex]l[/tex] is the distance covered by the car before it slowed down
[tex]\frac{1}{2} m v_i^2 = m* \mu_k * g * l[/tex]
=> [tex]l = \frac{v_i^2 }{2 * \mu_k * g }[/tex]