Resolve Kinematics Problem: x, h, g

[FlukeATX]

[Resolved] Kinematics problem?

Homework Statement

A small ball rolls horizontally off the edge of a tabletop of height h. It strikes the floor a distance x horizontally away from the edge of the table. (a) How long is the ball in the air? (b) What is its speed at the instant it leaves the table? Please give your answer in terms of the given variables and g.

Homework Equations

I'm not sure, since there's no numbers involved and it just wants symbolic answers. I'd think it'd be one of the standard kinematics formulas, but there's only two knowns, acceleration and displacement.

The Attempt at a Solution

I have no idea where to start. There is no initial velocity given, no final velocity given, and no time given (in fact, that's what the question is looking for). So, how can this problem be solved if there are only two knowns? It's not the fact that they're looking for the answers in terms of x,h,g that's bothering me, I'm not sure how to approach this even if there was actual values.

Any help is appreciated!

 

[LowlyPion]

Welcome to PF.

What they want you to do is express the distance, which is the horizontal velocity times the time for it to fall to the floor.

The time you can figure from the height.

 

[FlukeATX]

But the problem is that I do not know the horizontal velocity. I suppose this could be found by dividing the distance by the time, but I am not sure how to find the time. You say it can be found by the height, but how? Am I on the right track here:

Vy = 0
d = h
a = g = -9.8
t = ?

d=Vyt + 1/2gt^2
d=1/2gt^2
2d=gt^2
2d/g=t^2
t=sqrt(2d/g)

Does that make sense?

Then I could find the horizontal velocity by:
Vx=d/t
Vx=d/(sqrt(2d/g))Sound right?

[edit]
Just submitted it through the wileyplus system and the above is correct. Thanks for the help, got the wheels turning!

 

[LowlyPion]

Thanks for the help, got the wheels turning!

That of course is the idea.

Congrats and good luck.