A 3.39-kg block is sliding down a 7.92-kg frictionless incline. Both are initially moving to the right at 10.3 m/s. q7 (a) If the block ends up moving to the right at 21.4 m/s on the horizontal surface, determine the final velocity of the incline (in m/s).

Final Speed of Incline = 5.549 m/s

Explanation:

To answer this question, we must remember the fact that any momentum gained by the block is equal to the momentum lost by the incline.

So lets start by find the initial and final momentum of the box in the horizontal direction:

Initial Momentum = mass * initial velocity

Initial Momentum = 3.39 * 10.3 = 34.917 kg*m/s

Final Momentum = mass * final velocity

Final Momentum = 3.39 * 21.4 = 72.546 kg*m/s

Change in momentum: 72.546 - 34.917 = 37.629 kg*m/s

This is equal to the momentum lost by the incline.

Initial momentum of incline = 7.92 * 10.3 = 81.576 kg*m/s

Final momentum of incline = 81.576 - 37.629 = 43.947 kg*m/s

Plugging this into the momentum equation to find the speed:

Final Speed * Mass = Final Momentum

Final Speed = 43.947 / 7.92

Final Speed = 5.549 m/s