The car A of mass 1500 kg, travelling at 25 m/s collides with another car B of mass 1000 kg travelling at 15 m/s in the same direction. After collision the velocity of car A becomes 20 m/s. Calculate the velocity of car B after the collision.

Explanation

In order to solve this problem, we will calculate the total momentum of both the cars, before and after the collision.
(a) `underset(("before collision"))("Momentum of car A")=underset("car A")("Mass of")xxunderset("car A")"Velocity of"`
`=1500xx25`
=37500 kg.m/s
`underset(("before collision"))("Momentum of car B")=underset("car B")("Mass of")xxunderset("car B")"Velocity of"`
`=1000xx15`
=15000 kg.ms
Total momentum of car A and car B=37500+15000
(before collision)=52500 kg.m/s
(b) After collision,the velocity of car A of mass 1500 kg becomes 20 m/s.
So, Momentum of car A=`1500xx20`
(after collision)=30000 kg.m/s
After collision, suppose the velocity of car B of mass 1000 kg becomes v m/s
So, Momentum of car B=`1000xxv`
(after collision)=1000 v kg.m/s
Total momentum of car A and B = 30000+1000 v.......(2)
(after collision)
Now, according to the law of conservation of momentum :
Total momentum=Total momentum
before collision after collision
That is, 52500=30000+1000 v
1000 v=52500-30000
1000 v=22500
`v=22500/1000`
v=22.5 m/s
Thus, the velocity of car B after the collision will be 22.5 m/s.