WAEC 2018 · Paper 2 · Q8

Momentum, projectiles, work & energy

A body of mass $20\text{ kg}$ moving with a velocity of $80\text{ m s}^{-1}$ collides with another body of mass $30\text{ kg}$ moving with a velocity of $50\text{ m s}^{-1}$ . If the two bodies moved together after collision, find their common velocity if they moved in the:

(a)
same direction before collision;
(b)
opposite directions before collision.

Worked solution (try it first)

(a)

Same direction: $20(80) + 30(50) = (20 + 30)v$ .
$1600 + 1500 = 50v$ , so $v = 62\text{ m s}^{-1}$ .

(b)

Opposite directions: $20(80) + 30(-50) = 50v$ .
$1600 - 1500 = 50v$ , so $v = 2\text{ m s}^{-1}$ , in the direction the $20\text{ kg}$ body was moving.

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