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Q.

A spot light S rotates in a horizontal plane with a constant angular velocity of 0.1 rad/s. The spot of light P moves along the wall at a distance 3m. What is the velocity of the spot P when $θ = 45^{0}$

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a

0.6 m/s

b

0.5 m/s

c

0.4 m/s

d

0.3 m/s

answer is A.

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Detailed Solution

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$\cot θ = x / 3 \Rightarrow x = 3 \cot θ$

$\frac{d x}{d t} = 3 (- {cosec}^{2} θ \frac{d θ}{d t})$

$V = 3 {cosec}^{2} 45 \times (- 0.1) = - 3 \times 2 \times - 0.1$

$V = 0.6 m / s$

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