Conservation of momentum of a frog jump

AI Thread Summary
In the discussion about the conservation of momentum during a frog's jump from a plank, the problem involves calculating the minimum speed required for the frog to successfully jump to the other edge of the plank, which is floating on water. The solution relies on the conservation of momentum and energy principles, leading to the formula sqrt((MgL)/(m+M)) for the minimum speed. Participants clarify that the "minimum speed" refers to the take-off speed rather than the speed at the highest point of the jump. Additionally, the center of mass of the system is considered to determine the necessary jump distance. The discussion emphasizes understanding the dynamics of the frog's jump in relation to the moving plank.
Luca 123
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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]
 
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What have you tried?

Have you determined how far the frog must jump?
 
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.
 
Luca 123 said:
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.
 
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