Small block with velocity inside a large block at rest

[CoconutFred]

Homework Statement

Homework Equations

(Conservation of momentum)
(Conservation of energy)

The Attempt at a Solution

I know linear momentum must be conserved on the X-axis, so

mv_o=mv_1x+Mv₂

where v₁ is the final velocity of the small mass and v₂ is the final velocity of the large mass. Also, M=2m.

Energy is also conserved, so

(1/2)mv_o²=(1/2)mv₁²+(1/2)Mv₂²+mgR

Since the problem stipulates that the 2 blocks never lose contact with each other, I'm guessing the momentum in the x direction would actually be

mv_o=(m+M)v₂

and v₂=v_1x

But I'm not sure if that is right, and so I'm not totally sure where to go from here.

 

[Herman Trivilino]

It looks like you have all the physics in place to solve it. Keep going with the algebra ...

When I solved it I wrote everything in terms of the velocity $\vec{v}$ of the small block, so that

$v^{\ 2}=v_x^{\ 2}+v_y^{\ 2}.$

 

[J Hann]

I don't think that momentum is conserved in the x-direction.
What can one say about conservation of momentum in the y-direction?
Also, the two blocks do not form an isolated system because of the normal
force on the larger block by the frictionless surface.

 

[Herman Trivilino]

I don't think that momentum is conserved in the x-direction.
What can one say about conservation of momentum in the y-direction?

There are no external forces in the x-direction.
There are external forces in the y-direction.

Also, the two blocks do not form an isolated system because of the normal
force on the larger block by the frictionless surface.

That normal force is one of the external forces in the y-direction.