Conservation of a mechanical energy question

[wilmerena]

Hi, this is my first time here and Id like to thank in advance for any help offered
Im having trouble with the following question about 2 masses in an atwoods machine.

2 masses are initially at rest at the same height, if m2 has a given initial upward speed, how high does m2 rise above its initial position before momentarily coming to rest, (masses for each are given with m2 being heavier)

I know that I need to show some work before I should post this, but I embarrased to say I don't know how to even apporach it

any tips will be greatly appreciated

 

[arildno]

Welcome to PF!
This is a conservation of mechanical energy question.
Set up the initial mechanical energy of the whole system (kinetic+potential)
When the system falls momentarily at rest (assuming that the string remains taut all the time), the system only have potential energy.
As a hint, note that with a taut, inextensible string, the increase of height for m2 must equal the decrease of height for m1

 

[e(ho0n3]

First, find the acceleration of the masses. Then use some kinematics to find the distance. Should be dead easy.