A stationary firework explodes into three pieces. The masses and the velocities

Q#23 (Past Exam Paper – March 2017 Paper 12 Q10)

A stationary firework explodes into three pieces. The masses and the velocities of the three pieces immediately after the explosion are shown.


What are speed vand speed v2?




Solution:
Answer: B.


From the conservation of momentum,

Sum of momentum before explosion = Sum of momentum after explosion


The momentum before the explosion is zero as the firework was stationary.

Momentum is a vector quantity, so we need to consider the directions.

The momentum vector can be broken down into 2 components: horizontal and vertical.


Consider the vertical components:

{Momentum = mv}

Downward momentum = 100 × 8 = 800 g ms-1

Sum of upward momentum = 50v1 sin 60° + 50v2 sin 60°

Sum of upward momentum = downward momentum

50v1 sin 60° + 50v2 sin 60° = 800

(v1 + v2) 50sin 60° = 800

v+ v2 = 800 / 50sin 60°

v+ v2 = 18.48                        eqn (1)


Consider the horizontal components,

50 × v1 cos 60° = 50 × v2 cos 60°
v1 = v2                                    

So, the speeds v1 and v2 are equal. Consider equation (1) again,

v1 + v1 = 18.48                        (since v1 = v2)

2v1 = 18.48

Speed v1 = 18.48 / 2 = 9.24 m s-1

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