Two particles P and Q have masses 4m and m respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2013 - Paper 1

To find the speed and direction of particle Q after the collision, we can apply the principle of conservation of momentum. The momentum before the collision can be expressed as:

$$4m(2u) + m(5u) = 8mu + 5mu = 13mu$$

Let the speed of Q after the collision be ( v ). The momentum after the collision is:

$$4m(\frac{1}{2}u)(-1) + mv = -2mu + mv$$

Setting the total momentum before and after the collision equal gives:

$$13mu = -2mu + mv$$

Rearranging this equation:

$$v = 13mu + 2mu$$ $$v = 15mu$$

Since momentum is conserved, the direction of Q after the collision will be opposite to its initial direction, so after the collision, Q is moving in the same direction as P was initially. Thus, the speed of Q is ( 5u ) and its direction is reversed.

Therefore, the speed of Q after the collision is ( 5u ) in the direction opposite to its initial direction.