Two particles $P$ and $Q$ are moving in a straight line on a smooth horizontal plane with velocities $u_{1}$ and $u_{2}$ respectively. The two particles collide directly. Immediately after the collision, the velocities of $P$ and $Q$ are $v_{1}$ and $v_{2}$ respectively.

The coefficient of restitution between $P$ and $Q$ is given by

$e = \frac{Speed of separation}{Speed of approach} = \frac{v_{2} - v_{1}}{u_{1} - u_{2}} .$

Find the coefficient of restitution for each of the scenarios:

Immediately before the collision,

P

and

Q

are moving in the same direction with speeds 5 m s^-1 and 2 m s^-1 respectively. Immediately after the collision,

P

and

Q

are moving in the same direction with speeds 3 m s^-1 and 4 m s^-1 respectively.

ii)

Immediately before the collision,

P

and

Q

are moving in opposite directions with speeds 5 m s^-1 and 2 m s^-1 respectively. Immediately after the collision,

P

and

Q

are moving in opposite directions with speeds 3 m s^-1 and 4 m s^-1 respectively.

iii)

Immediately before the collision,

P

and

Q

are moving in opposite directions with speeds 5 m s^-1 and 2 m s^-1 respectively. Immediately after the collision,

P

and

Q

move with speeds 3 m s^-1 and 4 m s^-1 respectively. The direction of motion of

P

is unchanged but the direction of motion of

Q

is reversed.

Collisions (Edexcel International A Level Maths: Mechanics 2)

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