Question

A 4.80-kg ball, moving to the right at a velocity of +1.70 m/s on a frictionless table, collides head-on with a stationary 7.75-kg ball. Find the final velocities of the balls if the collision meet the following conditions.

(a) elastic

4.8-kg ball	=_________ m/s
7.75-kg ball	=_________ m/s

(b) completely inelastic _________m/s

Answer 1

b) completely inelastic collision

momentum conservation

=> 4.80*1.7 + 0 = (4.8 + 7.75)*v

=> v = 0.650 m/s

a) elastic collision

momentum conservation

4.80*1.7 + 0 = 4.80*v1 + 7.75*v2 .....eq1

energy conservation

0.5*4.80*(1.7)^2 + 0 = 0.5*4.80*v1^2 + 0.5*7.75*(v2)^2

=> 13.87 = 4.80*v1^2 + 7.75*(v2)^2

put value of v1 from eq1

=> 13.87 = 4.80*[(8.16 - 7.75*v2)/4.8]^2 + 7.75*(v2)^2

=> this quadratic equation , we can find value of v2 and then v1 also.