Two balls of equal mass are thrown horizontally with the same initial velocity. they hit identical stationary boxes resting on a frictionless horizontal surface. the ball hitting box 1 bounces back, while the ball hitting box 2 gets stuck. 1)which box ends up moving faster?

The box 1 moves faster.

Explanation:

lets

Mass =m  kg

Initial velocity = u m/s

Initial velocity of box = 0 m/s

Let stake mass of block = m

When ball bounces back:

The final speed of the box = v

Final speed of ball = - u

Pi = Pf  ( From linear momentum conservation)

m x u + m x 0 = m ( - u) + m v

mu + mu = m v

v= 2 u

When ball get stuck :

The final speed of ball and box = v

Pi = Pf  ( From linear momentum conservation)

m x u + m x 0 = (m+m) v

v= u /2

So the box 1 moves faster.