(a) A body of mass 3kg moves with a velocity of 8ms\(^{-1}\). It collides with...
(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.