A particle is moving along the curve y= 5*sqrt{4 x + 4}. As the particle passes through the point (3, 20) its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
I solved this problem and my answer yielded me: 10
However the computer isn't accepting this I must have done something wrong...
Thanks!
so you were correct in finding dy/dt, the problem was the question was not asking for dy/dt. it was asking for the rate at which the line connecting the origin and the point (3,20) was changing. as with all related rates problems, ALWAYS DRAW A DIAGRAM, that way you can see clearly what you have and what you want to find
Jhevon when you get a word problem -one such as this- ,or any other related rates problem in general what are you looking for? What steps do you typically work through in order to find the answer. I am very good at differentiation w/ respect to time (t), however sometimes the wording can make the problem seem somewhat trivial. Especially when I am the one having to set it all up. What is your method? Thanks as always!
When it comes to related rates, there is pretty much one way to go. the solution i gave to this problem illustrates that method. the steps to solving any related rates problem are as follows:
1) Read the problem carefully. Sounds trivial, but reading for math is different from other types of reading. make sure you understand what the question is asking for and what info it is giving you to find what it's asking for.
2) Draw a diagram. 99% of related rates problem have some form of diagramatical interpretation. Draw a diagram to see what's going on. If you had drawn a diagram for this problem, you would not have made the mistake of thinking dy/dt was what you needed to find. you would realize immediately that the distance between the point and the origin was the line i called z. Ths step is very important and can save you a lot of headaches.
3) Label Stuff. After drawing your diagram, give stuff names to keep track of them. write the labels on your diagram, write everything you know and everything you want to find, this includes both the magnitudes of the components you are dealing with and the rates at which they are changing.
4) Come up with a formula that relates what you know to what you don't know. You should try to get a formula with the least amount of unknowns possible. Sometimes it is hard to find such a formula and you would have to solve for one variable in terms of another you know about. You see for this question, the formula I came up with was pythagoras' theorem, it related all my knowns to my unknowns. this is usually the formula to use when you diagram has a triangle in it, but at other times, especially when you are dealing with the angles in a triangle, you would have to use the law of cosines or the law of sines etc.
5) Differentiate both sides of the formula you come up with with respect to t. You are good at this, no explanation necessary
6) Substitute your knowns and solve for the unknowns. Note that most of the time you will have an unknown that was not given to you, but you can use the formula you came up with to find it. In this problem, we were not told the length of z, but once i had my formula, i could find it.
And that's it, you follow that pattern with every related rates problem. I did quite a few related rates problems on this site. Look around and you can see this method in action. You will realize i follow the same pattern each and every time, no exceptions. If you have trouble finding them, just tell me and I'll help you look them up.