WAEC 2016 · Paper 2 · Q7

(a)
A body of mass $3\text{ kg}$ moves with a velocity of $8\text{ m s}^{-1}$ . It collides with a second body moving in the same direction with a velocity of $5\text{ m s}^{-1}$ . After collision, the bodies move together with a velocity of $6\text{ m s}^{-1}$ . Find the mass of the second body.
(b)
If the second body in (a) moves with a velocity of $5\text{ m s}^{-1}$ in the opposite direction to the $3\text{ kg}$ body moving at $8\text{ m s}^{-1}$ , find, correct to two decimal places, the common velocity of the two bodies if they move together after collision.

Worked solution (try it first)

Now the $6\text{ kg}$ body moves the other way: momentum before $= 3(8) + 6(-5) = -6$ .
After: $(3 + 6)v = 9v$ , so $v = -\dfrac69 = -\dfrac23$ .
The common velocity is $0.67\text{ m s}^{-1}$ , in the direction the $6\text{ kg}$ body was moving.