Find actual speed of jeep. Assume that police jeep is on axis of the mirror.

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Solution

Given: A thief is running away in a car with velocity of 20 m/s. A police jeep is following him, which is sighted by thief in his rear view mirror which is a convex mirror of focal length 10 m. He observes that the image of jeep is moving towards him with a velocity of 1cm/s. If the magnification of the mirror of the jeep at that time is 1/10. The police jeep is on axis of the mirror.
To find the actual speed of the jeep.
Solution:
Focal length of the convex mirror, $f = 10 m$
Velocity of image of jeep with respect to mirror, $V_{i / m} = - 1 c m / s = - 10^{- 2} m / s$ as it is moving towards the mirror.
magnification of the mirror, $m = \frac{1}{10}$
Velocity of mirror with respect to ground = velocity of car, $V_{m / g} = 20 m / s$
Let velocity of jeep with respect to mirror, $V_{o / m}$
According to velocity formula,
$(V_{i / m})_{⊥} = - m^{2} (V_{o / m})_{⊥} ⟹ - 10^{- 2} = - \frac{1}{10^{2}} (V_{o / m})_{⊥} ⟹ (V_{o / m})_{⊥} = + 1 m / s = + 1^i$
Let velocity of jeep with respect to ground be, $V_{o / g}$
$_{o / g} =_{o / m} +_{m / g} = + 1 + 20 = (+ 21 m / s)^i$
Hence the actual speed of the jeep is 21m/s.

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