A street light is mounted at the top of a 14 ft pole. A man 5 ft tall walks away from the pole at a rate of 4 ft per second. How fast is the tip of his shadow moving when he is 50 ft from the pole?

Question

Speed of tip of shadow: ________ft per second

Answer 1

Draw a figure: a right triangle with altitude 14 and base x+y=p, where y is the distance from the pole to the man and x is the distance from the man to the shadow tip.

First observe that dp/dt=(dy/dt)+(dx/dt)

Then 14/(x+y) = 5/x =>14/5=(x+y)/x

Subtract 1 from each side of the equation to get 9/5=y/x so that

dy/dt=(9/5)(dx/dt)

Substitute in the first equation to get dp/dt which you will see is independent of the man's position.

dx/dt=4 ft/sec

dy/dt=(36/5) ft/sec

Can you at least add the 2?