What is the velocity of a ball on a frictionless curved track?

[boxcarracer767]

I am stuck on this problem:

A ball with a mass of M is on a frictionless curved track with a radius of R. The track sits atop a table that has height of H. Solve the following in terms of R,g,H, and M.
a) the velocity of the ball
b) the time it takes to hit the floor
c) the distance D the ball lands from the base of the table
d)the total amount of energy the ball has when it strikes the floor

Here are my answers, are these correct.
a) v= sqrt(2gH) ?
b) t=sqrt(2gh)/g ?
c)?
d) would i add 1/2mv^2 + MgR+MgH ?

 

[James R]

You've told us the track is on the table, and the ball is on the track. What's this about the ball hitting the floor? And the velocity could be anything, from the information you have given.

 

[boxcarracer767]

I have attached a diagram to show what I am trying to solve for, and the velocity is as the ball leaves the table.

 

[boxcarracer767]

Ive tried to work out the problem , can anyone see if these answers are correct.
a)sqrt(2gR)=velocity
b)sqrt(2H/g)=time
c)H+ R =distance
d)mgh=total energy

Thanks

 

[James R]

a) the velocity of the ball

Assuming it is released from rest at the top of the track, and the track is frictionless, the speed as it leaves the track will be sqrt(2gR).

b) the time it takes to hit the floor

Your answer is correct.

c) the distance D the ball lands from the base of the table

Answer is:

sqrt(4RH)

d)the total amount of energy the ball has when it strikes the floor

Answer is mg(H + R), taking the zero of potential energy to be floor level.