Thread: Function Problem

A street light is 12 feet above a straight bike path. Olav is bicycling down the path at a rate of 15 MPH. At midnight, Olav is 39 feet from the point on the bike path directly below the street light. (See the picture.) The relationship between the intensity C of light (in candlepower) and the distance d (in feet) from the light source is given by C = (k/d^2), where k is a constant depending on the light source.



a) From22 feet away, the street light has an intensity of 1 candle. What is k?
22^2 = k = 484

b) Find a function which gives the intensity I of the light shining on Olav as a function of time t, in seconds.

So below is the answer for "b" but I am confused on how to get this, can someone explain to me? Thank you!

From the result of part a), we know:



Using the Pythagorean theorem, we may state:



where is the distance from the point directly below the lamp that Olav is at at time .

If midnight is set to time , then we have:

where

Thus:

and so:



and thus, we find:

Thank you so much!