# Optimization(?) Problem

1. Dec 11, 2005

### seiferseph

A particle is travelling along the postivie x axis at a constant speed of 5 units per second.

a) Where is the point when its distance from the point (0, 1) is increasing at a rate of 4 units per second?

b) Where is the point when its distance from the point (0, 1) is increasing at a rate of 6 units per second?

I am completely stuck, I could use some hints, thanks!

2. Dec 11, 2005

### Tom Mattson

Staff Emeritus
Start by writing down a function for the distance between the particle and the point (0,1) as a function of time.

And no, this is not an optimization problem.

3. Dec 11, 2005

### seiferseph

one sec i'll post some stuff i was trying, and the question isn't optimization but i'm not really sure how to classify it

4. Dec 11, 2005

### seiferseph

here is the diagram i have

since the y coordinate is constant, dy/dx is zero
dx/dt = 5, and ds/dt = 4

so s^2 = (x - 0)^2 + (y - 1)^2
after taking the derivative of s = sqrt(x^2 + (y - 1)^2 and putting in the y point as y = 0
i get
ds/dt = x *dx/dt / sqrt(x^2 + 1)

which, solving for x after putting in the dx/dt and ds/dt gets
x = 3/4
y = 0

as the point, is that correct?

5. Dec 11, 2005

### seiferseph

actually this would be a related rates problem then