A particle is headed into a corner as shown with momentum pi

A particle is headed into a corner as shown, with momentum p_i. If the collisions with the walls are elastic, what is the particle\'s final momentum? The dashed lines are qualitative, but the walls make a right angle with one another.

Solution

As the collision is elastic, the magnitude of the momentum remains same. But the direction is reversed.

Hence the momentm after collision is -p_i