A person reaches a maximum height of 65cmwhen jumping straight up from a crouche

Question

A person reaches a maximum height of 65cmwhen jumping straight up from a crouched position. During the jump itself, the person's body from the knees up rises a distance of around 46cm . To keep the calculations simple and yet get a reasonable result, assume that the entire bodyrises this much during the jump.

a) With what initial speed does the person leave the ground to reach a height of 65cm ?

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

Explanation / Answer

a) Apply energy conservation

0.5*m*v^2 = m*g*h

==> v = sqrt(2*g*h)

= sqrt(2*9.8*0.46)

= 3 m/s

b) contact time is needed.

F*t = m*(v2 - V1)

F = m*v/t

= m*g*v/(g*t)

= W*v/(g*t)

so we need t, then only get answer for part B

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