Question

A lamp of negligible height is placed on the ground 'h' metre away from a wall. A man "I" metre tall is walking at a speed of l/10 m/sec. from the lamp to the nearest point on the wall. When he is mid-way between the lamp and the wall, the rate of change in the length of this shadow on the wall is.

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Answer 1

A lamp of negligible height is placed on the ground 'h' metre away from a wall. A man "I" metre tall is walking at a speed of l/10 m/sec. from the lamp to the nearest point on the wall. When he is mid-way between the lamp and the wall, the rate of change in the length of this shadow on the wall is.

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Answer 2

Explanation:

Since, the two triangles are similar,

l

1

h

=

x

l

2

⇒h=

x

l

1

l

2

⇒

dt

dh

=−

x

2

l

1

l

2

dt

dx

(As h is decreasing)

Given, x=

2

l

1

and

dt

dx

=

10

l

1

So,

dt

dh

=−

5

2l

2

m/sec