# Problem: 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 75-kg man just before contact with the ground has a speed of 5.5 m/s. (a) In a stiff-legged landing he comes to a halt in 1.5 ms. Find the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.08 s. Find 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 force of the ground on the man in parts (a) and (b).

###### FREE Expert Solution

In this problem, we'll consider the upward direction as positive.

Change in momentum:

$\overline{)\begin{array}{rcl}\mathbf{m}{\mathbf{v}}_{\mathbf{f}}\mathbf{-}\mathbf{m}{\mathbf{v}}_{\mathbf{0}}& {\mathbf{=}}& \mathbf{F}\mathbf{∆}\mathbf{t}\end{array}}$

(a)

From the change in the momentum equation, we can solve for F as:

$\begin{array}{rcl}\mathbf{m}\mathbf{\left(}{\mathbf{v}}_{\mathbf{f}}\mathbf{-}{\mathbf{v}}_{\mathbf{0}}\mathbf{\right)}& \mathbf{=}& \mathbf{F}\mathbf{∆}\mathbf{t}\\ \mathbf{F}& \mathbf{=}& \frac{\mathbf{m}\mathbf{\left(}{\mathbf{v}}_{\mathbf{f}}\mathbf{-}{\mathbf{v}}_{\mathbf{0}}\mathbf{\right)}}{\mathbf{∆}\mathbf{t}}\\ & \mathbf{=}& \frac{\mathbf{\left(}\mathbf{75}\mathbf{\right)}\mathbf{\left[}\mathbf{0}\mathbf{-}\mathbf{\left(}\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{5}\mathbf{\right)}\mathbf{\right]}}{\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}}\end{array}$

92% (230 ratings) ###### Problem Details

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 75-kg man just before contact with the ground has a speed of 5.5 m/s.

(a) In a stiff-legged landing he comes to a halt in 1.5 ms. Find the average net force that acts on him during this time.

(b) When he bends his knees, he comes to a halt in 0.08 s. Find 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 force of the ground on the man in parts (a) and (b).

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Our tutors have indicated that to solve this problem you will need to apply the Intro to Impulse concept. You can view video lessons to learn Intro to Impulse. Or if you need more Intro to Impulse practice, you can also practice Intro to Impulse practice problems.