Skier A of mass 71kg slides down a slope and makes a completely inelastic collision with Skier B, who is stationary, and has a mass of 55kg.Immediately after the collision both skiers have a speed of 5.8m/s.
a)Find the speed of skier A immediately before the collision. (I got this part, 10.3m/s)
b) If skier A slid down the hill with a starting velocity of 0m/s, what is the vertical height of the slope? (I don't get this one, I tried with y=v^2/2g and got 5.4 but its not the right answer)
b.
Assuming a) is correct, then
1/2 m vf^2=mgh (ke at bottom=pe at top)
h=1/2 vf^2/g=about 10.3^2 /2*9.8=5.41
I am wondering about significant digits. Your speed after collision is two digits, yet you got correct the part a) with three digits...Then you put in two digits for a)...
I'm guessing the answer sheet has some mistake? It says the height is 9.6m , which I can't seem to figure out how they got that number! :s
To find the vertical height of the slope, you can use the law of conservation of energy. Under the assumption that there is no energy loss due to friction or air resistance, the initial potential energy of skier A will be equal to the final kinetic energy of both skiers after the collision.
Let's denote the height of the slope as h, the initial speed of skier A as v1, and the final speed of both skiers as vf.
The initial potential energy of skier A is given by mgh, where m is the mass of skier A and g is the acceleration due to gravity.
The final kinetic energy of both skiers is given by (m1 + m2)vf^2, where m1 is the mass of skier A, m2 is the mass of skier B, and vf is the final speed of both skiers.
Using the conservation of energy equation, we can equate these two expressions:
mgh = (m1 + m2)vf^2
Substituting the given values:
m = 71 kg
m1 = 71 kg
m2 = 55 kg
vf = 5.8 m/s
We can rearrange the equation and solve for h:
h = [(m1 + m2)vf^2] / (mg)
h = [(71 kg + 55 kg)(5.8 m/s)^2] / (71 kg * 9.8 m/s^2)
h = (126 kg)(33.64 m^2/s^2) / (693.8 kg*m/s^2)
h ≈ 6.09 m
Therefore, the vertical height of the slope is approximately 6.09 meters.
To solve part (b) of the problem, you need to use the conservation of mechanical energy principle. The initial potential energy of Skier A, when they start at rest, is converted into kinetic energy as they slide down the slope, given by the equation:
Initial Potential Energy = Final Kinetic Energy
The potential energy is given by the equation: Potential Energy = mass * gravitational acceleration * height.
The kinetic energy is given by the equation:
Kinetic Energy = 0.5 * mass * velocity^2
Set the initial potential energy equal to the final kinetic energy:
mass * gravitational acceleration * height = 0.5 * mass * velocity^2
To cancel out the mass on both sides of the equation, divide both sides by the mass:
gravitational acceleration * height = 0.5 * velocity^2
Now, you need to solve for the height of the slope.
Given:
gravitational acceleration = 9.8 m/s^2 (acceleration due to gravity)
velocity = 5.8 m/s (final speed of both skiers)
height = ?
Substituting the given values into the equation, we get:
9.8 * height = 0.5 * 5.8^2
Simplifying further:
9.8 * height = 0.5 * 33.64
Solving for height:
height = (0.5 * 33.64) / 9.8
height ≈ 1.71 meters
Therefore, the vertical height of the slope is approximately 1.71 meters.