Question

An average person can reach a maximum height of about 60 cm when jumping straight up from a crouched position. during the jump itself, the person's body from the knees up typically rises a distance of around 50 cm. to keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump.

Answer 1

1) You can find the velocity with which the jumper leaves the ground by using the formula for the final velocity of an upward vertical motion.

Vf^2 = Vo^2 - 2gd

The data known are: Vf = 0, g = 9.81 m/s^2,   and d = 60 cm = 0.6 m

=> Vo^2 = 2gd = 2*9.81m/s^2 * 0.6 m = .11.772 m^2/s^2 =>

Vo = 3.4 m/s

2) You can obtain the acceleration of the jumper during the jump by using the equivalent formula, Vf^2 = Vo^2 + 2ad

Where, Vf^2 is the velocity with which he leaves the ground (3.4 m/s), Vo is zero because he jumps from the rest, d is the distance that his body rises from knees,which is 50 cm = 0.5 m

Then,  a = Vf^2 / 2d = [3.4m/s]^2 / (2*0.5m) =   11.6 m/s^2

And now, you can find the force exerted by the jumper as:

F = m*a, and if you know his weight, W = m*g => m = W/g

Replace m in F = m*a => F = W*a/g = W*11.6m/s^2 / 9.81 m/s^2 = 0.10 W

F = 0.10 W