Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at the western- most point of the track, and, at the same time, Alexandra started at the northernmost point. They both run counterclockwise. Alexandra runs at 4 meters per second, and will take exactly 2 minutes to catch up to Charlie. Impose a coordinate system, and give the x- and y-coordinates of Charlie after one minute of running.
I have no idea how to start when I have info. only for Alexandra....
Google your question or whatever search engine you have. A university math site will come up with that question on their assignment page. The answer is at the end of the question. If you can't find it let me know.
The answer isn't the whole thing, I would like to understand how to do a problem like this, if possible. Also this question is more complex than the examples shown in my book which is why I was looking for some help.
Yes, I can certainly understand that. Sometimes teachers have to defer to other ones when they have a little less knowledge and no one is stepping up to the plate.
Why don't you post your question again? There are other teachers who may have missed the chance to help you.
To solve this problem, let's start by establishing a coordinate system.
We can place the center of the circular track at the origin (0,0) of our coordinate system. The western-most point where Charlie starts would correspond to the x-coordinate (-60,0), and the northernmost point where Alexandra starts would correspond to the y-coordinate (0,60).
Since Charlie is running counterclockwise on the circular track, his position after one minute would correspond to an angle of 1/30th of a full revolution (since he is running at a constant speed of 60 seconds per revolution).
To find Charlie's x and y coordinates after one minute, we can use trigonometry. Since the radius of the track is 60 meters, the angle corresponding to one minute of running for Charlie would be (1/30) * 2π radians.
Using the trigonometric functions sine and cosine, we can calculate the x and y coordinates as follows:
x-coordinate of Charlie after one minute = (-60) * cos((1/30) * 2π)
y-coordinate of Charlie after one minute = 60 * sin((1/30) * 2π)
Let's calculate these coordinates using a calculator:
x-coordinate of Charlie after one minute = (-60) * cos(2π/30) ≈ 55.66
y-coordinate of Charlie after one minute = 60 * sin(2π/30) ≈ 19.32
So, after one minute of running, Charlie's coordinates are approximately (55.66, 19.32).