A man of height 2m walks directly away from a lamp of h
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A man of height 2m walks directly away from a lamp of height 5m, on a level road at 3 m/s. The rate at which the length of his shadow is increasing is
A.
1m/s
B.
2m/s
C.
3m/s
D.
4m/s
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Let be the lamp and PQ be the man and OQ=x metre be his shadow and let MQ =y metre.
∴dydt=speed of the man
=3 m/s (given)
∵ΔOPQ and ΔOLM are similar
∴OMOQ=LMPQ⇒x+yx=52⇒y=32x∴dydt=32dxdt⇒3=32dxdt⇒dxdt=2m/s