Question

A red, 0.05-kg croquet ball moving at +10 m/s collides with a stationary green bocci ball (m = 0.100 kg) in a frictionless elastic collision, What is the speed of each ball immediately after the collision?

Answer 1

velocity of red ball is either 0 or 1 m/s and then the velocity of green ball is 10 m/s or 8 m/s.

Step-by-step explanation:

mass of red ball, m1 = 0.05 kg u 1 = 10 m/s

mass of green ball, m2 = 0.1 kg, u2 = 0

Let the velocity of red ball and green ball after the collision is v1 and v2, respectively.

By use of conservation of momentum

m1 u1 + m2 u2 = m1 v1 + m2 v2

0.05 x 10 + 0 = 0.05 x v1 + 0.1 x v2

0.5 = 0.05 (v1 + 2 v2)

v1 + 2v2 = 10 ...... (1)

Now use conservation of kinetic energy

1/2 m1 x u1^2 + 1/2 x m2 x u2^2 = 1/2 m1 v1^2 + 1/2 m2 x v2^2

0.05 x 10 x 10 + 0 = 0.05 x v1^2 + 01. x v2^2

5 = 0.05(v1^2 + 2v2^2)

10 = v1^2 + 2 v2^2 .....(2)

Put teh value of v1 from equation (1) in equation (2)

10 = 10 - 2 v2 + 2 v2^2

0 = v2^2 - v2

v2 =0 , 1 m/s

So, v1 = 10 - 2 x 0 = 10 m/s

or v1 = 10 - 2 x 1 = 8 m/s

Thus, the velocity of red ball is either 0 or 1 m/s and then the velocity of green ball is 10 m/s or 8 m/s.