Two questions Speed question, momentum in collisions

[dud8118]

1.A particle starts out at rest at point A at the top of a smooth curved track of vertical height 40cm.
a> what is its speed at the bottom of the curved track? b> How far along the adjoining inclined plane, which makes an angle of 30 degree with the horizontal, will the particle go, assuming that all contacts are smooth?

2.Consider a light weight marble of mass m rolling at a speed of 20cm/s toward a very messive metallic sphere of the same size and of mass M suppose that as result of the collision the marble come to rest. a> what is the final velocity of the metallic sphere? b> Assuming the radii of the sphere are very small, calculate the kinetic energy lost by the system in this collision.

I attached the diagram which i drew poorly sorry Please help me, this is my review for the test. I have test tommorow and I tried to look for simliar problem on web and searching through the book for hint but i just can't grasp this... these are two questions i have left... that i couldn't solve it

 

[fatra2]

1. simple conservation of energy problem. You don't have friction, therefore, you are in conservative problem.

2. simple conservation of momentum problem. What happens before and after the collision should be equivalent.

Whether the size of the sphere, kinetic energy is not lost. It can be transform into another form of energy.

Cheers