A student (m = 66 kg) falls freely from rest and strikes the ground. During the collision with the ground, he comes to rest in a time of 0.04 s. The average force exerted on him by the ground is +18000 N, where the upward direction is taken to be the positive direction. From what height did the student fall? Assume that the only force acting on him during the collision is that due to the ground.
Here is my work. Can't figure out what I am doing wrong.
18000 N => Average force
0.04 s=> Time
66kg => Mass
Average force*time = M*Vf -M*Vo
18000*0.04 = 66*Vf - 66*0
10.91 = Vf
Vf = 2h/t
10.91 = 2h/0.04
h = 0.218
Figured it out!
(V impact)^2/(2*g)
V impact = (F ground*t)/m
=6.07 m
Your calculation for the final velocity (Vf) is correct, but you made an error in calculating the height (h). Let's go through the problem step-by-step to find the correct height.
Given:
Mass (m) = 66 kg
Average force (F_avg) = 18000 N
Time (t) = 0.04 s
Step 1: Calculate the final velocity (Vf)
Use the equation F_avg * t = m * Vf - m * Vo, where Vo is the initial velocity (0 m/s) since the student falls from rest.
18000 N * 0.04 s = 66 kg * Vf - 66 kg * 0
720 Ns = 66 kg * Vf
Solve for Vf:
Vf = 720 Ns / 66 kg
Vf ≈ 10.91 m/s
Step 2: Calculate the height (h)
Use the equation Vf^2 = 2gh, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
(10.91 m/s)^2 = 2 * 9.8 m/s^2 * h
119.0281 m^2/s^2 = 19.6 m/s^2 * h
Solve for h:
h = 119.0281 m^2/s^2 / 19.6 m/s^2
h ≈ 6.08 m
Therefore, the correct height from which the student fell is approximately 6.08 meters.
Your calculation for the final velocity (Vf) is correct, which is 10.91 m/s. However, there seems to be an error in your calculation for the height (h).
To find the height from which the student fell, you can use the equation of motion:
Vf^2 = Vo^2 + 2g*h
where Vf is the final velocity (which is 0 m/s since the student comes to rest), Vo is the initial velocity (which is 0 m/s since the student falls freely from rest), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
In this case, the equation becomes:
0 = 0^2 + 2*9.8*h
Simplifying the equation, we get:
0 = 19.6h
Dividing both sides by 19.6, we find:
h = 0
According to the equation, the height from which the student falls is 0. This means that the student is on the ground already and the collision is happening at ground level.