Question

A cube with mass M slides down a frictionless curved incline as shown in the
figure below. It has a completely inelastic collision with another cube m at the bottom that is

Answer 1

The other guy is being a smart alec.

a) Velocity of mass M when it reaches mass m is found by using the conservation of energy.

Height energy lost = Kinetic energy gained

M . g . h = 0.5 . M . V^2

V = ?( 2 . g . h ) = ? ( 2 . 9.8 . 0.3 ) = 2.4 m/s

b) Momentum is conserved and Kinetic energy is conserved

M . 2.4 = M . V1 + m . V2

0.5 . M . 2.4^2 = 0.5 . M . V1^2 + 0.5 . m . V2^2

Sub M/2 = m and cancel all M's

2.4 = V1 + V2/2

2.4^2 = V1^2 + V2^2/2

You can solve this pair of equations - it leads to a quadratic that probably needs the formula to sort it out. But it actually factorises easily.
And V1 = 2.4 / 3 = 0.8 m/s

V2 = 2.4 . 4 / 3 = 3.2 m/s

These speeds make sense. The little mass m is smacked by a big mass and so takes off quickly. The big mass M runs into the little mass. M slows down but still keeps going at some reduced speed.

Now the two masses fly over the edge of the table. They both take the same time to drop to the floor

t = ? (2 . h / g) = ?( 2. 0.9 /9.8 ) = 0.43 s

During this time the masses will travel sideways with the speed they acquired from the collision.

Distance from the table M lands is 0.43 . 0.8 = 0.34 m

Distance from the table m lands is 0.43 . 3.2 = 1.37 m