# A boy jumps from a wall 3m high. What is an estimate of the change in momentum of the boy when he lands without rebounding?

## A. 5 N/s B. 50 N/s C. 500 N/s D. 5000 N/s The answer is C, but why?

Dec 10, 2017

See explanation.

#### Explanation:

It is not possible to give the answer as an exact number if the boy's mass is not given.

The boy's end velocity can be calculated using the energy preservation law:

## ${E}_{k} = {E}_{p}$

The equation comes from the fact that all boy's initial potential energy is transferred to kinetic energy.

## $v = \sqrt{2 g h} \approx 7 , 75$

So the change in momentum is:

$\Delta p = 7.75 m$

where $m$ is the boy's mass.

Looking at the answers we find that if the mass is about $64.5 k g$ then the answer would be $C$. Other answers require boy to be too heavy ($640 k g$ for answer $D$) or too light ($6.4 k g$ for $B$ or $0.64 k g$ for $A$).

The second part (referring to answers $A$ and $B$) comes from the fact that new born kids usually weigh about $4$ kg, so a kid weighing $6.4$ kg is in an age he usually can't walk or jump.