Question

A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of the streetlight is 15 feet, what is the rate at which the person's shade is lengthening?

The answer is actually 2.667 ft/sec but I have no idea what the process should be. If you can help please do, thank you!!

Answer 1

use similarity to get the equation of walking away and the shadow then just differentiate both sides, then put the value`

Answer 2

If you want a method to solve questions like these, the first thing you need to do is this:

Don't freeze.

Just start it and go. Just like when someone asks you, hey, what's 52 times 32? You don't know, and it would be crazy if you just knew by looking at it and you'd be a genius. But I know I'm not, but that doesn't stop me from starting the process of writing one number under the other, start multiplying each digit etc... and then I get the answer to 52*32. You should really think of this like that.

So what's that way of thinking?

1. List out all the values of things mentioned in the problem. If it says a length or distance, call it L=52 meters or Distance = 45 yards or whatever. This is preference, but the thing is, once you have everything important listed with some kind of unit and easy to use name or variable, you're fairly good to go.

2. Draw out a picture. It doesn't have to be perfect, just approximate. Don't worry about wasting paper, and don't try to be a doctor. What do I mean by that? If the thing says it's a plane or a guy walking, then draw a little plane or person! Don't just draw a plain boring triangle. Then, try as best as you can to label them with the values from part 1.

The point of 1 & 2 is that they get you to start putting down concrete things and get as much of the problem's useful information out of your head and onto paper in front of you so that relationships between them become easier to see. Every problem where someone walks away from something will probably have a right triangle in it, right? The point is, you probably know a lot about right triangles, but not everything is going to be useful right now, and looking at a labelled shape gives you an idea of what formulas you might need. So start writing out the pythagorean theorem or a trig function of some angle in terms of your labelled variables in part 1.

Try solving. Think about the shapes. What do you _really_ need to do here? The rate something changes with respect to time, well consider differentiating the whole thing by time. Some things might seem odd, like the height of a lamp, how much does that change with respect to time? It doesn't since it's constant, so obviously the derivative is 0!

I hope this helps give you a feel for how to approach these rather than just seeing it and thinking, oh no, I'm totally hosed.

Answer 3

I thought at first I could solve this "related rate" problem, but became confused when there was no information regarding the location of the individual. However, the advice of Kainui is excellent, and maybe I don't need the location.......but still can't work it lol

Answer 4

hey sorry I forgot to put in the picture that was given.
but i will try solving