Acrobat & Monkey: Max Height Reached

[Mr Davis 97]

Homework Statement

A circus acrobat of mass $M$ leaps straight up with initial velocity $v_0$ from the trampoline. As he rises up, he takes a trained monkey of mass $m$ off a perch at a height $h$ above the trampoline. What is the maximum height attained by the pair?

Homework Equations

The Attempt at a Solution

This is a pretty simple problem. All we do is derive a new initial velocity from the conservation of momentum, and then calculate the h that results when the masses are combined. However, I am wondering why using the conservation of momentum is justified, since the system is not isolated because there is gravity acting in the y-direction. Thus, why can I use the conservation of momentum in the y-direction when the man and monkey collide?

 

[gneill]

What is the assumption that is made for the time it takes for a collision to occur? What change in gravitational PE is expected over that time interval?

 

[Mr Davis 97]

What is the assumption that is made for the time it takes for a collision to occur? What change in gravitational PE is expected over that time interval?

Ah, okay. So in the very small limit of the time of collision momentum is conserved.

 

[gneill]

Ah, okay. So in the very small limit of the time of collision momentum is conserved.

Right. In particular, it occurs in a small enough time interval that there is no work done by gravity during the process as the objects don't move (noticeably) higher or lower in the gravitational field.