Question

A 100 g ball moving to the right at 4.2 m/scatches up and collides with a 450 g ball that is moving to the right at 1.2 m/s .

a) If the collision is perfectly elastic, what is the speed of the 100 g ball after the collision?

b) If the collision is perfectly elastic, what is the speed of the 450 g ball after the collision?

Answer 1

Since the collision is perfectly elastic and the collision takes place in a straight line, the relative velocities are related by, v2-v1 = -(u2-u1), where u1 and u2 are velocities of ball 1 and 2 before collision and v1 and v2 are the velocities after collision.

=> v2-v1 = -(1.2-4.2) = 3m/s => v2 = v1+3 -------------- 1

Now, by conservation of momentum, m1u1+m2u2 = m1v1+m2v2

=> (0.1*4.2)+(0.45*1.2)=(0.1*v1)+(0.45*v2)

=> 0.96 = 0.1v1+0.45v2

From 1, v2 = v1+3, Hence, 0.96 = 0.1v1+0.45v1+1.35 => 0.55v1 = 0.39 => v1 = 0.709m/s

Hence, velocity of 100 g ball is 0.709m/s

Therefore, v2 = 0.709+3 = 3.709m/s.

Hence velocity of 450 g ball is 3.709 m/s