39.1k views
1 vote
A street light is at the top of a 11 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 feet from the base of the pole

User Crasher
by
4.8k points

1 Answer

7 votes

Answer:

8.8ft/s

Explanation:

Height of pole=11 foot

Height of man=6 foot

Let x be the distance of man from the pole and y be the distance of tip of shadow from the base of the pole.


(dx)/(dt)=4 ft/s

Two right triangles are similar then the ratio of their corresponding sides are equal


(6)/(11)=(y-x)/(y)


6y=11y-11x


11x=11y-6y=5y

Differentiate w.r.t t


11(dx)/(dt)=5(dy)/(dt)


11* 4=5(dy)/(dt)


(dy)/(dt)=(11* 4)/(5)=8.8ft/s

Hence, the tip of her shadow is moving at the rate 8.8ft/s when she is 45 feet from the base of the pole

A street light is at the top of a 11 foot tall pole. A 6 foot tall woman walks away-example-1
User Dmfrey
by
5.5k points