• Dec 2nd 2006, 09:07 PM
Tascja
A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Find the rate of change of the length of his shadow when he is 4 m from the light.

so far i have the the ratio is that the shadow is 15/2 when he is 4 m away. but when i plug in to get the rate of change im way off...

With the similar triangle do i have to compare the shadow to the length they give me or to his height???
• Dec 3rd 2006, 12:28 AM
earboth
Quote:

Originally Posted by Tascja
A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Find the rate of change of the length of his shadow when he is 4 m from the light.

so far i have the the ratio is that the shadow is 15/2 when he is 4 m away. but when i plug in to get the rate of change im way off...

With the similar triangle do i have to compare the shadow to the length they give me or to his height???

Hello Tascja,

I've attached a sketch of the situation.

t: elapsed time
2*t: length of the way the man has walked in t seconds.

The length of the shadow can be calculated:

$\frac{S}{15}=\frac{2}{4+2\cdot t}$. Solve for S:

$S=\frac{30}{4+2\cdot t}=\frac{15}{2+ t}$

The first derivative of S will give the rate of change:

$S'(t)=-\frac{15}{(2+t)^2}$

EB