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Wednesday, January 22, 2020

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


Question 23
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 v1 and speed v2?






Reference: Past Exam Paper – March 2017 Paper 12 Q10





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
v1 + v2 = 800 / 50sin 60°
v1 + 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

2 comments:

  1. mass should be converted from grams to kg

    ReplyDelete
    Replies
    1. there is no need in this case as we are not calculating the actual momentum. rather, we are equating terms.

      even if we had converted the mass, it would cancel on both sides

      Delete

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