A lamp is shining on top of a vertical light post that is 540 centimetres tall. A girl is running away from the base of the light post at a constant rate so that her shadow is increasing at the rate of 15 cm/s and the tip of her shadow is moving away from the base at the rate of 90 cm/s. How tall is she?

Question

Quizplus · Accepted Answer

The Answer is Let x be length of shadow, y be the distance from the tip of the shadow to the base of the light post and L be the girl's height (as shown in the figure below).
From similarity,

Let x be length of shadow, y be the distance from the tip of the shadow to the base of the light post and L be the girl's height (as shown in the figure below). From similarity, = ; hence 540 x = L y; L is a constant! Differentiating both sides with respect to time we obtain 540 = L Substituting = rate of change of shadow = +15 cm / s and = rate of change of distance between the tip of the shadow and the base of the light post = + 90 cm /s, we obtain 540(15) = L (90). Therefore L = = 90 cm. The girl is 90 cm tall (about 3 feet ).

=

; hence 540 x = L y; L is a constant!
Differentiating both sides with respect to time we obtain 540

= L

Substituting

= rate of change of shadow = +15 cm / s and

= rate of change of distance between the tip of the shadow and the base of the light post = +
90 cm /s, we obtain 540(15) = L (90). Therefore
L =

= 90 cm.
The girl is 90 cm tall (about 3 feet ).

A Lamp Is Shining on Top of a Vertical Light