(a) A body of mass 3kg moves with a velocity of 8ms(^{-1}). It collides with a second body moving in the same direction with a velocity of 5ms(^{-1}). After collision, the bodies move together with a velocity of 6ms(^{-1}). Find the mass of the second body.
(b) If the second body in (a) moves with a velocity of 5ms(^{-1}) in the opposite direction as that of the 3kg body with a velocity of 8ms(^{-1}), find, correct to two decimal places, the common velocity of the two bodies if they move together after collision.
Explanation
(a)
Momentum before collision = Momentum after collision.
(((3 times 8) + 5m) = (3 + m) times 6)
(24 + 5m = 18 + 6m)
(24 – 18 = 6m – 5m implies m = 6kg)
(b)
Momentum before collision = Momentum after collision
((3 times 8) – (5 times 6) = (3 + 6)v)
(-6 =9v)
(implies v = -0.67ms^{-1})
The bodies move in the direction of the second body.