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 v0 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.
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 v1 = Mv0/(M+m).
Since they reach a maximum height v2/2g + x0 the height attained is
xmax = v12/2g + hm/(M+m) = M2*v02/(M+m)2/2g + hm/(M+m)
The first term is right here. The second is not.
Secondly i use energy conservation:
Wbefore = mgh + Mv02/2
Wafter = (M+m)gxmax
xmax = hm/(M+m)+Mv02/2(M+m)g
The right answer is v02M2/(M+m)2/2g+h(1- M2/(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.