Question

Numerical A lamp is hanging from the top of a post of height 4 m from the ground. A man of height 1.6 m is walking away from the post with a speed of 2 m/s as shown in the figure. What will be the speed of the tip of his shadow, nearest to an integer? AB = 1.6 m and OL=4m
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Answer 1

Consider the fig,

Let x be the distance of the man from the pole at time t.

Let s be the length of the shadow at time t.

△CED∼△AEB from AAA Postulate

⟹

CD

CE

=

AB

AE

1.6

s

=

8

x+s

5s=x+s

s=

4

1

x

The man is walking at the speed of 0.5m/s

dt

dx

=0.5

Rate of change of length of the shadow is

dt

ds

=

dx

ds

dt

dx

=

dx

d

(

4

1

x) 0.5

=

4

1

×0.5=0.25

∴ Rate at which the shadow is increasing is 0.25 m/s