9702/Oct Nov/13/2017/Q10

Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together.

What is the speed of the trucks after the collision?

Solution:
Answer: A

In order to solve this question we need to use the principle of conservation of momentum which states:

The momentum in a closed system remains constant before and after a collision or explosion.

I.E.

momentum before=momentum after

And ingeneral momentum is calculated using: P=mv where P is the momentum, m is the mass of the object, and v is the velocity of the object.

Hence the total momentum before the collision is:

P1+P2
=(m x 2v) + (3m x (-v))

NOTE: notice the negative v on the second truck as it is moving in the opposite direction to the first truck
=-mv

After the collision the the trucks stick together so the total mass becomes 4m and the combined trucks move at an unknown speed of v_​after

We will solve the equation for conservation of momentum to determine v_after​:

mv=4mv_after

cancelling out the m's:

v=4v_after

and rearranging to make v_​after the subject of the equation:

v_after​=0.25v

Which is our final answer.

Reference: PYQ - Oct/Nov 2017 Paper 13 Q10