hamza_b23 2 years ago Please help on related rates i do not get it A light is fastened on a rolling cart 1m above the floor. The light moves at 2m/s towards a 2m tall man standing 4m from a wall. How fast is the tip of the mans shadown on the wall moving when the light is 7m from the wall?

1. hamza_b23

@phi

2. Kelumptus

This resource will help you with these kinds of problems: http://www.intmath.com/applications-differentiation/4-related-rates.php. Generally the first step with these kinds of problems is to simply draw a picture. In this case the picture will look something like this:

3. Kelumptus

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4. Kelumptus

So what we have done in this picture already is that we have found the variables and the constants of the problem. The variables being x & y and the constants being the measurements given in the picture and speed that the cart is moving at. Note that the speed is given as -2. It is negative because as the cart moves closer to the man, x gets smaller. We will refer to the speed of the cart as: $\frac{ dx }{ dt }$ (change in x with respect to t or time)

5. Kelumptus

The next step now is to build a mathematical relationship between x and y. Looking at the picture we can see that there is actually a triangle inside a triangle (see http://www.youtube.com/watch?v=1T9dHMU5pkk). So we can then say: $\frac{ y-1 }{ 1 }=\frac{ 4+x }{ x }$ We say y -1 because we don't want to the first meter and we define y to start from the ground up, not from the height of the light.

6. Kelumptus

See how you go from here and let me know if you get stuck and i will give you some more help =)