Question

question 10
problem reference 7.1
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 75.0 kg man just before contact with the ground has a speed of 6.40 m/s. in a stiff - legged landing he comes to a halt in 2.00 ms (milliseconds). when the man bends his knees, he comes to a halt in 0.100 s.
what is the average net force that acts on him when he lands stiff - legged?
240 n
1540 n
240,000 n
480 n

Explanation:

Step1: Calculate the change in momentum

The formula for momentum is \(p = mv\). The initial velocity \(v_{i}=6.40\ m/s\) and the final velocity \(v_{f} = 0\ m/s\). The mass \(m = 75.0\ kg\).
The change in momentum \(\Delta p=m(v_{f}-v_{i})=75.0\times(0 - 6.40)=- 480\ kg\cdot m/s\)

Step2: Use the impulse - momentum theorem

The impulse - momentum theorem is \(J=\Delta p=F_{avg}\Delta t\).
For the stiff - legged landing, \(\Delta t = 2.00\times10^{-3}\ s\)
We can solve for \(F_{avg}\): \(F_{avg}=\frac{\Delta p}{\Delta t}\)
Substitute \(\Delta p=- 480\ kg\cdot m/s\) and \(\Delta t = 2.00\times10^{-3}\ s\) into the formula:
\(F_{avg}=\frac{-480}{2.00\times10^{-3}}=- 240000\ N\)
The negative sign indicates the direction of the force (opposite to the direction of initial velocity). The magnitude of the average net force is \(240000\ N\)

Answer:

240,000 N