Question

Car A hits car B (initially at rest and of equal mass) from behind while going 15 m/s Immediately after the collision, car B moves forward at 10 m/s and car A is at rest. What fraction of the initial kinetic energy is lost in the collision?

Answer 1

Given :

Initial speed of car A is 15 m/s and initial speed of car B is zero.

Final speed of car A is zero and final speed of car B is 10 m/s.

To Find :

What fraction of the initial kinetic energy is lost in the collision.

Solution :

Initial kinetic energy is :

`K.E_i = (15^2m)/(2) + 0\\\\K.E_i = (225 m)/(2)`

Final kinetic energy is :

`K.E_f = (10^2m)/(2) + 0\\\\K.E_f = (100m)/(2)`

Now, fraction of initial kinetic energy loss is :

`Loss = ((225m)/(2)-(100m)/(2))/((100m)/(2))\\\\Loss = (125)/(100)\\\\Loss = 1.25`

Therefore, fraction of initial kinetic energy loss in the collision is 1.25 .