1. HELP!!! Circle problem

This is the problem:

Quinn is running aruond the circular track x^2 + y^2 = 10,000, whose radius is 100 meters, at 4 meters per second. Quinn starts at the point (100,0) and runs in the counterclockwise direction. After 30 minutes of running, what are Quinn's coordinates?

Okay first off, please don't flat out give me the answer cuz I want to do it myself. But I really just don't get how to do it!! So can someone please explain this to me?

Okay, so one, how do I draw the x^2 + y^2 = 10,000? Is it just a regular circle, the center at the origin, with an 100 meter radius?

And two, how do I find Quinn's coordinates on the graph? Once I get the circle set up, I'll be able to calculate his distance around the circle I'm sure, but how do I find the exact coordinates?

THANK YOU SO MUCH, if someone could answer within an hour or two I would be really appreciative, it is pretty urgent

2. Originally Posted by pyrosilver
This is the problem:

Quinn is running aruond the circular track x^2 + y^2 = 10,000, whose radius is 100 meters, at 4 meters per second. Quinn starts at the point (100,0) and runs in the counterclockwise direction. After 30 minutes of running, what are Quinn's coordinates?

Okay first off, please don't flat out give me the answer cuz I want to do it myself. But I really just don't get how to do it!! So can someone please explain this to me?

Okay, so one, how do I draw the x^2 + y^2 = 10,000? Is it just a regular circle, the center at the origin, with an 100 meter radius?

And two, how do I find Quinn's coordinates on the graph? Once I get the circle set up, I'll be able to calculate his distance around the circle I'm sure, but how do I find the exact coordinates?

THANK YOU SO MUCH, if someone could answer within an hour or two I would be really appreciative, it is pretty urgent
Yes, the circle has its center at (0,0) and its radius is 100 meters.
Then the initial position of the runner, (100,0), means he is at the point (100,0), . On your drawing , that is at x=100, y=0. Or it is at the x-axis, 100 m from the (0,0).

Then he ran at 4 m/sec counterclockwise for 30 minutes or (30*60) = 1800 seconds.
What is the final position Of Quinn then in coordinates form?

It is easier for me to explain it with computations but you want to do it yourself so....

3. Originally Posted by ticbol
Yes, the circle has its center at (0,0) and its radius is 100 meters.
Then the initial position of the runner, (100,0), means he is at the point (100,0), . On your drawing , that is at x=100, y=0. Or it is at the x-axis, 100 m from the (0,0).

Then he ran at 4 m/sec counterclockwise for 30 minutes or (30*60) = 1800 seconds.
What is the final position Of Quinn then in coordinates form?

It is easier for me to explain it with computations but you want to do it yourself so....
Okay, so he goes 7200 meters in 30 minutes?

So the track is 628.3 meters, right? That means that he goes around 11.459 times. So he goes around 11 times. Then, do I multiply 628.3 and .459? I got 288.390.

If all that is correct, how do i find the coordinate of it?

Thanks by the way for replying, I'm really relieved.

4. Originally Posted by pyrosilver
Okay, so he goes 7200 meters in 30 minutes?

So the track is 628.3 meters, right? That means that he goes around 11.459 times. So he goes around 11 times. Then, do I multiply 628.3 and .459? I got 288.390.

If all that is correct, how do i find the coordinate of it?

Thanks by the way for replying, I'm really relieved.
Okay. My computations say it is 288.5 m past the positive x-axis.
Meaning, the runner is at 288.5 m counterclockwise from his starting point.

One way to get that position is by using proportion.
One revolution, or one circumference, is for 360 degrees.
So for 2888.5 m arc, that would be for angle theta
theta / 288.5 = 360 / 200pi
theta = 360(288.5 / 200pi) = 165.3 degrees.

That means the runner is in the 2nd quadrant.
Its y-coordinate is 100*sin(165.3 deg) = 25.38 m.
Its x-coordinate is 100cos(165.3 deg) = -96.73 m
Therefore, the runner now is at (-96.73, 25.83) ----answer.

5. Originally Posted by ticbol
Yes, the circle has its center at (0,0) and its radius is 100 meters.
Then the initial position of the runner, (100,0), means he is at the point (100,0), . On your drawing , that is at x=100, y=0. Or it is at the x-axis, 100 m from the (0,0).

Then he ran at 4 m/sec counterclockwise for 30 minutes or (30*60) = 1800 seconds.
What is the final position Of Quinn then in coordinates form?

It is easier for me to explain it with computations but you want to do it yourself so....
Originally Posted by ticbol
Okay. My computations say it is 288.5 m past the positive x-axis.
Meaning, the runner is at 288.5 m counterclockwise from his starting point.

One way to get that position is by using proportion.
One revolution, or one circumference, is for 360 degrees.
So for 2888.5 m arc, that would be for angle theta
theta / 288.5 = 360 / 200pi
theta = 360(288.5 / 200pi) = 165.3 degrees.

That means the runner is in the 2nd quadrant.
Its y-coordinate is 100*sin(165.3 deg) = 25.38 m.
Its x-coordinate is 100cos(165.3 deg) = -96.73 m
Therefore, the runner now is at (-96.73, 25.83) ----answer.
Aah, I think i got it now. Thank you SO MUCH for taking the time to help me out!! i appreciate it A LOT!