Question

# A man, 1.6m tall, walks away from a lamp which is 4m above ground, at the rate of 30m/min.If his shadow increases at the rate of λ m/min, then the value of λ is

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Solution

## Let PQ=4m be the height of lamp and AB=1.6m be height of man. Let the end of shadow is R and it is at a distance of I from A when the man is at a distance of x from PQ, at some instance. Since △PQR and △ABR are similar,Thus PQAB=PRAR ⇒41.6=x+ll ⇒2x=3l ⇒2dxdt=3dldt {∵dxdt=30m/min} ∴dldt=23⋅30m/min=20m/min(lengthening) Thus λ=20

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