Related Rates problems
I am greatly struggling with related rates problems. I'll give an example and perhaps someone can walk me through it.
At noon, ship A is 70 km west of ship B. Ship A is sailing south at 25 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 6:00 PM?
I don't even know where to begin really, according to my notes I should begin by writing down the given info and what I'm trying to find and drawing a picture of applicable, but after doing all this I still have no idea how to go about finding the answer. I know that da/dt would be 25 and db/dt would be 15, but I don't know how I would use that information at all. I also know that a triangle will be involved, but again I don't know how to use that information to solve this problem.
Ok so bottom line, based on the diagram, you want to find when - that's your question
So at 6pm, 6 hrs have passed; therefore, ship A has travelled 150km south (y1) and ship B has travelled 90 km north (y2). y= y1+y2=240km
x = 70km = CONSTANT
AT THE INSTANT of 6pm, z would be km
Therefore, to solve this question, you use a modified version of pythagorean's theorem:
Note: and are variables, NOT constants.
Plug in all your numbers and solve... should get km/h
I'm still very very confused. I understood everything up to the final two lines, the equation involving z^2=etc. I have no iea how you came up with that to solve it? I understand that the distance between the ships at 6pm is 250 km but I don't understand how to use that information to find the rate of change between the ships at that time.
you need to find a relationship between z, x, and y...there's a right angle triangle... seem fimilar to you?
Originally Posted by fattydq
Yes of course, but he already used the pythagorean theorem to find the 250km, I don't see how using the pythagorean theorem could possibly lead to the answer of the fraction he provided
Again I understand the whole thing until you involve the final step, the fraction.
Originally Posted by skeeter
take the derivative of D w/r to t using the chain rule ...