Question

question 12
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.
during the landing of the man, the average net force is the vector sum of the force of the ground on the man and the force due to gravity.
what is the force that the ground exerts on the man during the stiff - legged landing? you may disregard significant figure rules.
239,265 n
975 n
240,735 n
2,271 n

Explanation:

Step1: Calculate the acceleration

Using the formula \(a=\frac{v - u}{t}\), where \(u = 6.40\ m/s\), \(v=0\ m/s\), and \(t = 0.002\ s\) (since \(2.00\ ms=2\times10^{- 3}\ s\)).
\(a=\frac{0 - 6.40}{0.002}=-3200\ m/s^{2}\)

Step2: Apply Newton's second law \(F_{net}=ma\)

The mass \(m = 75.0\ kg\). So \(F_{net}=75\times(- 3200)=-240000\ N\)

Step3: Consider the force of gravity \(F_g=mg\)

\(F_g = 75\times9.8 = 735\ N\)

Step4: Find the force of the ground \(F_{ground}\)

Since \(F_{net}=F_{ground}-F_g\), then \(F_{ground}=F_{net}+F_g\)
\(F_{ground}=-240000 + 735=-239265\ N\). The magnitude is \(239265\ N\)

Answer:

239,265 N