Question 11
Two objects, each of mass 1.5 kg are moving in the same straight line but in opposite directions. The velocity of each object is $2.5 m s^{- 1}$ before the collision during which they stick together. What will be the velocity of the combined object after collision?

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Solution

Mass of one of the object, $m_{1} = 1.5$ kg
Mass of the other object, $m_{2}$ = 1.5 kg
Velocity of $m_{1}$ before collision, $u_{1}$ = 2.5 $m s^{- 1}$
Velocity of $m_{2},$ moving in opposite direction before collision, $u_{2}$ = -2.5 $m s^{- 1}$
Let v be the velocity of the combined object after collision.
By the law of conservation of momentum,
Total momentum after collision = Total momentum before collision,
Or, $(m_{1} + m_{2}) v = m_{1} u_{1} + m_{2} u_{2}$
Or, $(1.5 + 1.5) v = 1.5 \times 2.5 + 1.5 \times (- 2.5)$ [negative sign as moving in opposite direction]
Or, v = 0 $m s^{- 1}$

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