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Constrained Motion : General Approach

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Question

The reflection surface of a plane mirror is vertical. A particle is projected in a vertical plane which is also perpendicular to the mirror. The initial velocity of the particle is 10 m/s and the angle of projection is $60^{0}$ . The point of projection is at a distance 5m from particle moves towards the mirror . just before the particle touches the mirror. the velocity of approve of the particle and the image is :

A

10 m/s

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B

5 m/s

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C

10 \sqrt{3}

m/s

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D

5 \sqrt{3}

m/s

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Solution

The correct option is C 10 m/s
Horizontal component of the velocity is $10 c o s (60) = 5$
And vertical component is $10 s i n (60) = 8.66$
The participial will touch the mirror after $= \frac{5}{5} = 1 s$
In this time vertical velocity will be $V = u - g t = 8.66 - 9.8 \times 1 = - 1.14$
Now the relative velocity will be due to horizontal component of the particle .
Since the vertical velocity will be same .
So, te relative velocity of the particle is $2 \times 5 = 10 m / s$ .

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