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Q.

Image of an object approaching a convex mirror of radius of curvature 20m along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in 30 seconds. What is the speed of the object in km per hour?

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Detailed Solution

R = 20m, f = 10m
$\frac{1}{U_{1}} = \frac{1}{10} - \frac{3}{25} = - \frac{1}{50} \Rightarrow U_{1} = - 50 c m a n d \frac{1}{50 / 7} + \frac{1}{U_{2}} = \frac{1}{10} \Rightarrow U_{2} = - 25 c m$
$S o, s p e e d = | \frac{Δ U}{Δ t} | = \frac{25}{30} m / \sec = \frac{5}{6} m / \sec a n d i n k m / h r = \frac{5}{6} \times \frac{18}{5} = 3 k m / h r$

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Image of an object approaching a convex mirror of radius of curvature 20m along its optical axis is observed to move from 253m to 507m in 30 seconds. What is the speed of the object in km per hour?