Question

When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 63.5-kg man just before contact with the ground has a speed of 7.89 m/s. (a) In a stiff-legged landing he comes to a halt in 3.99 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.205 s. Find the magnitude of the average net force now. (c) During the landing, the force of the ground on the man points upward, while the force due to gravity points downward. The average net force acting on the man includes both of these forces. Taking into account the directions of the forces, find the magnitude of the force applied by the ground on the man in part (b).

Answer 1

a) F = 1.26 10⁵ N, b) F = 2.44 10³ N, c) F_net = 1.82 10³ N directed vertically upwards

Step-by-step explanation:

For this exercise we must use the relationship between momentum and momentum

I = Δp

F t = p_f -p₀

a) It asks to find the force

as the man stops the final velocity is zero

F = 0 - p₀ / t

the speed is directed downwards which is why it is negative, therefore the result is positive

F = m v₀ / t

F = 63.5 7.89 / 3.99 10⁻³

F = 1.26 10⁵ N

b) in this case flex the knees giving a time of t = 0.205 s

F = 63.5 7.89 / 0.205

F = 2.44 10³ N

c) The net force is

F_net = Sum F

F_net = F - W

F_net = F - mg

let's calculate

F_net = 2.44 10³ - 63.5 9.8

F_net = 1.82 10³ N

since it is positive it is directed vertically upwards