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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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
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