Conservation of momentum of a frog jump

[Luca 123]

Homework Statement

A frog of mass m jumps from the edge of a plank of mass M of length L to the other edge. The plank is on water and is free to move, assume no friction whatsoever. What is the minimum value of the speed of the frog ?

Homework Equations

Conservation of momentum and energy
Some kinematics equations
The answer given is sqrt((MgL)/(m+M))

The Attempt at a Solution

I think that the minimum speed means the magnitude of the velocity at the highest point, meaning Vx. But I cannot find [/B]

 

[gneill]

What have you tried?

Have you determined how far the frog must jump?

 

[AdityaDev]

Fix the end of plank without frog as (0,0) and let the frog be at (-L,0).
What will happen when the frog jumps?
What is center of mass of the system?
Using the center of mass, calculate the distance the frog has to jump.

 

[haruspex]

I think that the minimum speed means the magnitude of the velocity at the highest point

No, it means the minimum take-off speed. Remember that the frog can choose what angle to take off at.