A person reaches a maximum height of 61 cm when jumping straight up from a crouc

Question

A person reaches a maximum height of 61 cm when jumping straight up from a crouched position. During the jump itself, the person's body from the knees up rises a distance of around 45 cm . To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump.

Part A

With what initial speed does the person leave the ground to reach a height of 61 cm ?

Express your answer using two significant figures.

____________

Part B

In terms of this jumper's weight W , what force does the ground exert on him or her during the jump?

Express your answer using two significant figures.

____________

Explanation / Answer

PART: A

INTIAL SPEED V =SQUARE ROOT OF (2gh) = 3.5 m/s

PART: B

F = reaction of the ground
F = mg + ma

V² = 2ax (x = 0.45m)
a = V²/2x = 2gh/2x = gh/x
F = mg + mgh/x
F = W + Wh/x
F = W(1+h/x)
here
F = (1 + 0.61/0.45)W
F = 2.355 W

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