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A man of 2m walks directly away from a lamp of height 5m at rate of 7m/s . At what rate is the shadow is increasing.

A man of 2m walks directly away from a lamp of height 5m at rate of 7m/s . At what rate is the shadow is increasing.

Grade:12

1 Answers

Arun
25750 Points
6 years ago
h=2 m, H=5 m, v=7 m/s u=? 

x is the distance of man to lamp post, 
y is the distance from the tip of the shadow to the lamp post. 

From the similar triangles 
H/h = y/(y-x), 
5/2 = y/(y-x), 
5y -5x=2 y, 
3 y=5 x, 
0.6 y=x, 
d{0.6 y}/dt=dx/dt, 
0.6(dy/dt)=dx/dt, 
0.6u =v, 
u=v/0. 6=7/0.6=11.66 m/s.

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