A cat crouches on the floor, at a distance of 1.6 m from a desk chair of height .45 m. The cat jumps onto the chair, landing with zero vertical velocity. The desk chair has frictionless coasters and rolls away when the cat lands. The mass of the cat is 5.7 kg and the mass of the chair is 12 kg.

Question

What is the speed of recoil of the chair and cat?

Answer 1

The time of flight T to the chair can be deduced from the fact that the vertical velocity component is zero at elevation 0.45 m. Thus
(1/2)gT^2 = 0.45 m
T = 0.303 s
Since it travels 1.6 m in that time, you know the horizontal velocity component, 1.6/0.303 = 5.28 m/s

Use that initial (cat) velocity, the chair mass and the law of conservation of momentum to get the speed of recoil of the chair with the cat on it.

Answer 2

5.94m/s