Question

The figure below shows two crates gliding across a surface without any frictional interaction. Because the smaller crate is moving faster than the larger crate, at some time in the future, the smaller crate will collide with the larger one.

Answer 1

Take into account that the total momentum of the system is equal before and after the smaller crate collides with the larger crater.

Moreover, consider that after the collision, both craters move together.

Then, you have:

momentum before = m*2vi + 3m*vi = 5m*vi

momentum after = (m + 3m)v = 4m*v

If you equal the previous expressions:

4m*v = 5m*vi

By solving for v:

v = (5m*vi)/(4m)

v = 5vi/4

Hence, the speed of the two craters after the collision is 5/4 * vi