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## Homework Statement

I try to solve the problem 3.5 in Kleppner Kolenkow ”An introduction to Mechanics” using various approaches but end up with wrong answers. The problem is:

3.5 A circus acrobat of mass M leaps straight up with initial velocity v

_{0}from a 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

At first I use the fact that the center of mass is at

*hm/(M+m).*The velocity of the center of mass is

*v*

_{1}= Mv_{0}/(M+m).Since they reach a maximum height

*v*the height attained is

^{2}/2g + x_{0}*x*

_{max}= v_{1}^{2}/2g + hm/(M+m) = M^{2}*v_{0}^{2}/(M+m)^{2}/2g + hm/(M+m)The first term is right here. The second is not.

Secondly i use energy conservation:

*W*

W

_{before}= mgh + Mv_{0}^{2}/2W

_{after}= (M+m)gx_{max}This gives:

*x*

_{max}= hm/(M+m)+Mv_{0}^{2}/2(M+m)gThe right answer is

*v*

_{0}^{2}M^{2}/(M+m)^{2}/2g+h(1- M^{2}/(M+m)^{2})I know how to get to the right answer, but what I need is an explanation of what laws of physics i dont obey.