Find velocity of ball at end of inclined plane.?

Question

A ball starting from rest rolls down an inclined plane of height 1m. The inclined plane is sitting on a table. At the end of the inclined plane the ball becomes airborne (leaving at an angle of 20 degrees with respect to the floor). What is the ball's velocity as it becomes airborne? Assume mass of m kg.

Answer 1

You can solve this problem in terms of Energy.

So when the ball is at the top of the slope:

Its velocity is 0.

Therefore there is no kinetic energy only potential energy is present.

The potential energy with respect to the INCLINED PLANE is:

PE = mgh

since h = 1m

PE = mg

note: I say repect to the INCLINED PLANE because we do not include the height of the table. The height of the table does not matter because we only convert the energy of the inclined plane.

Now when the ball is airborn:

We assume it is at height = 0 m

therefore there is no PE but there is Kinetic Energy.

KE = 1/2mv^2

Since Energy is conserved.

PE = KE

mg = 1/2mv^2

rearrange:

v = squareroot(2mg/m) = squareroot(2g)