When jumping straight down, you can be seriously injured if you land stiff-legge

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 84.4-kg man just before contact with the ground has a speed of 6.41 m/s. (a) In a stiff-legged landing he comes to a halt in 1.36 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 0.245 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).

Explanation / Answer

a)

for initial speed , u = 6.41 m/s

t = 1.36 ms

Using first equation of motion

v = u +a * t

6.41 = 1.36 *10^-3 * a

a = 4713.2 m/s^2

magnitude of average net force = m * a

magnitude of average net force = 4713 * 84.4

magnitude of average net force = 3.98 *10^5 N

b)

for time t = 0.245 s

v = u +a * t

6.41 = 0.245 * a

a = 26.2 m/s^2

magnitude of average net force = m * a

magnitude of average net force = 26.2 * 84.4

magnitude of average net force = 2208 N

c)

for the force applied by ground,

for a)

force by ground = 3.98 *10^5 + 84.4 * 9.8

force by ground = 3.99 *10^5 N

for part b)

force by ground = 2208 + 84.4 * 9.8

force by ground = 3035 N

the force by ground is 3035 N

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