A ball moving with a momentum of 5 kg ms^–1 strikes against a wall at an angle of 45° and is reflected at the same angle. Calculate the change in momentum. 

Initial momentum is along AO. It has two rectangular components:

pcos45° along CO and psin45° along DO

Final momentum p is along OB. It has two rectangular components:

pcos45° along OC and psin45° along OE

Change in momentum along vertical direction 

= Final momentum – Initial momentum 

= psin45° - p sin45° = 0

Change in momentum along horizontal direction 

= – pcos45° - p cos45° = - 2pcos45°

=–2×5×1/√2= -2×5×0.707

= –7.07 kg ms^–1

Negative sign indicates that the direction of change in momentum is away from the wall.