Thread: derivative function

Q. A floodlight illumines a tall vertical wall that is 6 m from it. a man 2 m tall walks toward the wall in front of the light.
a) find a function that gives the height of his shadow as a function of his distance from the light.
Is this a formula I should know??

Originally Posted by smckinlay

Q. A floodlight illumines a tall vertical wall that is 6 m from it. a man 2 m tall walks toward the wall in front of the light.
a) find a function that gives the height of his shadow as a function of his distance from the light.
Is this a formula I should know??

No, but you should be able to construct it (this is the geometry part of the problem).

CB

I'm still lost. Assuming at 6 m the shadow is 2 m, and that as he approaches the wall the shadow increases - one point isn't enough to determine a function.

Originally Posted by smckinlay

I'm still lost. Assuming at 6 m the shadow is 2 m, and that as he approaches the wall the shadow increases - one point isn't enough to determine a function.

First, make a drawing of the situation (see attached image).
Let d be the distance of the man to the light (in meters) and the height of his shadow on the wall (again in meters). By similarity of the right triangles with legs 2 and d, and legs s(d) and 6, respectively, in such a drawing you find that , and, therefore, that .
So if the man stands right next to the wall, i.e. , we have , which seems reasonable enough.
If the man is sufficiently close to the light, i.e. , we have that , which may seem somewhat extreme but, if you think about it, isn't entirely unexpected either...