Question

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?

Answer 1

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.

`mgh=(mv^2)/2`

`v^2=2gh`

`v=sqrt(2gh)~~7,75`

So the change in momentum is:

`Deltap=7.75m`

where `m` is the boy's mass.

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