Solving a Lab to Place the Cup for the Ball

[Goodwillie7]

Homework Statement

I have a lab to do in which we have a ramp set up on a table. We are rolling the ball down the ramp, and letting it roll of the table. We have to figure out where to place the cup for the ball to roll into. If we do not get the ball in the cup we fail. How can I do that?

Homework Equations

All I know is the Initial velocity will be 0, since we are placing the ball at the top of the ramp then letting go. And once the ball rolls of the table, Acceleration is going to be -9.8m/s (squared)

The Attempt at a Solution

I would find the measurements of the ramp, the distance from the bottom of the ramp, to the end of the table, and the height of the table itself. Then use equations, but I don't know which ones.

 

[Astronuc]

Height of the ramp determines the GPE of the ball with respect to the table top, and that will be transformed into KE, from which one obtains a velocity in the horizontal, v_x.

When the ball leaves the table it falls under influence of gravity, so one must determine v_y(t), with v_y(0) = 0.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra11

and since the ball is rolling, there is rotational as well as translation KE.

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#cmi