1. ## particle velocity

A particle is moving along the curve below. y= root(x)
As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?

I appreciate the help

2. Originally Posted by winterwyrm
A particle is moving along the curve below. y= root(x)
As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?

I appreciate the help
this is a related rates problem. did you draw a diagram? (see below). you want the rate at which z is changing. can you figure out a relationship to relate x, y and z?

3. would it be pythagorean?

4. Originally Posted by winterwyrm
would it be pythagorean?
indeed! so we will use $z^2 = x^2 + y^2$

now what?

5. Thanks! I know how to do the rest, take the derivative, plug in known variables, then it goes back to algebra 1-2. I just have alot of trouble making the proper equation.

6. Originally Posted by winterwyrm
Thanks! I know how to do the rest, take the derivative, plug in known variables, then it goes back to algebra 1-2. I just have alot of trouble making the proper equation.
very good. when it comes to related rates, always draw a diagram if possible. as you can see, drawing that diagram allowed us to come up with Pythagoras' theorem as a way to relate the variables. if we had not drawn the diagram, we would probably not have known we were dealing with a triangle. so drawing the diagram is a good way to come up with what equation we should use, so remember that