A man 5 feet tall walks at a rate 5 feet per second away from a light that is 16 feet above the ground. When he is 8 feet from the base of the light, find the rate at which the tip of his shadow is moving.
everystepcalculus.com. Related Rates problem concerning a shadow of a man and a light pole. Index 8 to get to my menu. We’re going to scroll down to Related Rates, here. Here’s related rates there. Then we’re going to scroll down to shadow. Lamp post, person, shadow changing. Here’s a picture of it. And the lamp post is given as Alpha 16 feet high. You have to press Alpha before you enter anything into these entry lines, here. A mans rate of change is Alpha 5 and it is increasing because he is walking away from the lamppost. And the mans height is alpha 5 feet, the distance given is alpha 8. I always show you what you’ve entered, you can change it if you want. I say it’s okay. I show you the definitions of what we’re talking about. Now we do the calculations. You write all this on your paper, of course. Exactly as you see it. And so the change of is 88 over 11 feet per second. Now you can work this out if you want to, you know with a calculator. 88 divided by 11, this is the exact answer. And the second part of the problem. What’s the length of the shadow changing? And you do this calculation here. It turns out to be 25 over 11 feet per second. And you can do the approximation if you want on your calculator. Have a good one.