Question

person is jumping from a height ℎ0 = 10 m with zero initial velocity and a cricket ball is thrown directly upward with an initial velocity 𝑣𝑣0 = 9.8 m/s at the same instant when time t = 0 s as shown in Fig. 1. Consider h = 11.5 m and 𝚤𝚤̂and 𝚥𝚥̂ to be the unit vectors along the X and Y axis. Gravity is acting along the -𝚥𝚥̂direction and the magnitude of gravitational acceleration is given by g = 9.81 m/s2 . The red dot on the person represents his center of mass.

(a) (4 marks) If the person and the cricket ball consist of a system, find the position and velocity of the center of mass of the system at time t = 0.5 s.

(b) (2 marks) If it takes 0.01 seconds for the person to come to complete rest when he hits the ground, calculate the average force acting on the person.

(c) (4 marks) Now consider when the person hits the ground, he bends his knees such that the center of mass of his body is lowered by 15 cm. If the maximum force that the bone of his legs can withstand is 50000 N, will he break his legs?

Answer 1

$$mv=Ft\\m\sqrt{2gh}=Ft\\60\sqrt{2(9.81)(10)}=0.01F\\F=84\ kN$$

It is greater than 50000 N, thus he will break his legs.