Question

A body of mass 1 kg moving with velocity of 4 metre per second collides with a body of mass 0.5 kg moving with a velocity of 2m per second if the velocity of the first body after collision is 8/3 metre per second find the velocity of the second body after collision

Answer 1

Dear student,

Let us assume the collision to be elastic and the bodies move in the same direction. The kinetic energy is conserved.

Hence
Kinetic energy before collision= kinetic energy after collision

Kinetic energy of 1kg mass=1/2 mv²
=1/2 × 1 × 4²
= 8 Joules.

Kinetic energy of 0.5 kg mass:
= 1/2 × 0.5 × 2²
= 1 Joule.

Kinetic energy of 1 kg mass after collision:
= 1/2 × 1× (8/3)²
​​​​​​

= 32/9 joules.

Let the velocity of 0.5 of mass after collision be v
Then:

1+8= (32/9) + 1/2 ×0.5 × V²

= 9-(32/9) = 1/2 × 0.5 × V²

= (49/9) = 1/2 × 0.5 × V²

= V² = [(49/9)×2]/0.5

= V² = 196/9

= V= 14/3 m/s.