Question

A street light is at the top of a 22 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 7 ft/sec. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 50 ft away from the pole?

Answer 1

Answer:

Step-by-step explanation:

height of pole = 22 ft

height of girl = 5 ft

let the distance of girl from the foot to street light is x and the tip of shadow is at a distance from the street light.

dx / dt = 7 ft/s

By using the similarity of two triangles

$\frac{y-x}{5}=\frac{y}{22}$

22 y - 22 x = 5 y

17 y = 22 x

$y=\frac{22}{17}x$

Differentiate both sides with respect to t.

$\frac{dy}{dt}=\frac{22}{17}\times \frac{dx}{dt}$

$\frac{dy}{dt}=\frac{22}{17}\times 7$

dy/dt = 9.06 ft/s

Thus, the tip of the shadow is moving with speed 9.06 ft /s.