What Is the Speed of the Combined Blocks After Collision?

[zvee_y]

Homework Statement

A track consist of a frictionless arc XY, which is a quarter-circle of radius R, and a rough horizontal section YZ. Block A of mass M is releasecd from rest at point X, slides down the curved section of the track, and collides instantaneously and ineslastically with identical block B at point Y. The two blocks move together to the right. Express the answers in term of M, R, and g.
It asked to determind the speed of the combined blocks immediately after the collision.

Homework Equations

The Attempt at a Solution

Help me out please. This is the question from the AP test Physic B. I've tried to use the conservation of momentum after collision. But the initial velocity is 0, so how can i find the velocity after collision?Thank you

 

[Doc Al]

I've tried to use the conservation of momentum after collision.

Good. Momentum is conserved during the collision.

But the initial velocity is 0, so how can i find the velocity after collision?

The initial speed is 0 at the top of the arc, but the collision takes place at the bottom of the arc. Since the arc is frictionless, find the speed of block A when it reaches the bottom, just before it collides with block B.

 

[zvee_y]

so v=square-root-of 2gR
and the final velocity of 2 objects is vf=(square-root-of 2gR)/2
Is it right?

 

[Doc Al]

Right. That's the final speed of both blocks immediately after the collision.

 

[zvee_y]

Thank you!