A 70.0-kg man jumps 1.00 m down onto a concrete walkway.His downward motion stops in 0.04 seconds.If he forgets to bend his knees,what force is transmitted to his leg bones?
A) 700 N
B) 4000 N
C) 8000 N
D) 16,000 N

Question

Quizplus · Accepted Answer

We can use the impulse-momentum theorem to solve this problem.
Impulse = Change in Momentum
Impulse = Force x Time
Momentum = Mass x Velocity
Final Velocity = 0 m/s (as the man stops moving downwards)
Initial Velocity = ?
Initial Velocity can be found using the equation of motion:
y = vit + 1/2at^2
where y = 1 m, vi = ?, t = 0.04 seconds, and a = 9.8 m/s^2
Solving for vi, we get: vi = 9.9 m/s (approx.)
Momentum before jump = mv = 70 kg x 9.9 m/s = 693 kg m/s
Momentum after jump = 0 kg m/s
Change in momentum = -693 kg m/s
Impulse = Force x Time
-693 = F x 0.04
F = -693/0.04
F = -17,325 N
The force is negative because it is acting in the opposite direction to the man's vertical motion. Taking the magnitude of the force, we get 17,325 N, which is equivalent to 8000 N (approx.). Therefore, the best choice is C.

A 700-Kg Man Jumps 1