A 40 ton rail car and a 70 ton rail car initially at rest ar

A 40 ton rail car and a 70 ton rail car, initially at rest, are connected together with a giant but massless compressed spring between them. When released, the 40 ton car is pushed away at a speed of 4.5 m/s relative to the 70 ton car.

What is the speed of the 40 ton car relative to the ground?

Solution

Let the speed of 70 ton car relative to ground be x

So, the speed of the 40 ton car relative to ground = 4.5 - x

By conservation of momentum- ,

40*(4.5- x) = 70*x

So, 110x = 40*4.5

So x = 1.64 m/s

So, speed of 40ton car with respect to ground= 4.5 - 1.64 = 2.86 m/s