# Related rates

posted by
**Tracy**
.

Hey, I have a question on related rates and I'm a little rusty at them. I have an idea how to do this one but at a certian point i get stuck. The question is:

Two cars leave the intersection, the first travelling south at 40 km/hr and another travelling west at 90 km/hr. How fast is the distance between these cars increasing after 5 hours? Give your answer in km/hr.

So drawing the picture you get a triangle, and you can therefore say x^2 +y^2 = z^2 and we know the rates of which x and y are changing, and we are looking for the rate at which z is changing. So i know that much, the only thing that is getting me stuck is when it says after 5 hours. I thought of something like ifyou said x^2 + y^2 =5^2 then did that out and solved for one you could get something but I just got lost. I know I've done this before but I'm having a major block

z^2 = x^2 + y^2

differentiate, solve for dz/dt in terms of x, y, z, dx/dt, dy/dt You know what those are after five hours (distance=rate*time). z can be found from sqrt of sums of legs squared.

Ahhhh I knew I was missing something. Thanks a bunch, but I also have another question (I'm not doing too good one these realted rates).

A camera, located 2 km from the launch pad, is tracking the rocket that is fired straight up. When the height of the rocket is 20 km, the camera is rotating at the rate of 1/200 radians per second. What is the speed of the rocket at that instant? Give your answer in km/sec.

This is the same sort of thing right? The only thing that is stopping me is the whole radians per second. Would that mean that we would have to get trig into here somewheres. I mean I know its a triangle drawing so it would be possible, but radians really mess me up.