Which of the two following scenarios will cause the ship to be deflected off course the most?

Question

If a rocket ship (mass = M) is moving along through space and it gets hit on the side by a meteor (mass=m) (meteor’s velocity is perpendicular to that of the ship’s). Which of the two following scenarios will cause the ship to be deflected off course the most? Case 1: The meteor bounces elastically off of the ship – the meteor travels back in a direction from where it came. Case 2: The meteor sticks to the ship. Use conservation of linear momentum for each case and then compare the results.

Answer 1

I disagree with much of what TitoBob said. In an elastic collision, kinetic energy is conserved. No energy is converted into heat.

Elastic:
In cases where one mass has zero velocity (in the direction of the other mass) the equation becomes
V2 = 2*m*u1/(M+m)

Inelastic:
m*u1 + M*u2 = (m+M)*V2
V2 = m*u1/(m+M)

So the inelastic collision gives the rocket 1/2 of the velocity in the direction perpendicular to travel.

Answer 2

The energy of the meteor striking the space ship is fixed, and so is the amount of energy converted into heat. If it bounces off, part of the energy that's left will go back into the meteor to get it to move in the opposite direction. If it sticks to the ship (gets embedded into it), then all the energy that's left goes into changing the ship's direction, so that would cause the greatest deflection.