Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at the westernmost point of the track, and, at the same time, Alexandra started at the northernmost point. They both run counterclockwise. Alexandra runs at 3 meters per second, and will take exactly 2 minutes to catch up to Charlie.
Impose a coordinate system with units in meters where the origin is at the center of the circular track, and give the $x$- and $y$-coordinates of Charlie after one minute of running. (Round your answers to three decimal places.)
This is what I did:
Alex = $(0,60)$
Charlie = $(-60,0)$
The distance between the two is $20\cdot\pi\cdot\frac{60}{4}$ = $30\pi$
So if after two min $d=0$, after 1 min = $15\pi$ distance,
Alex= $3\frac{m}{s}\cdot60s= 180m$
Charlie = $180m+15\pi/120\pi = 0.6024648 \cdot 360^\circ = 216.88733855^\circ$.
Add $90^\circ$ (distance at inital)= $306.88733855^\circ$,$x=60\cos(306.88733855^\circ)= 32.984$
$y=60\sin(306.88733855^\circ)= -50.120$
This is wrong. Im really struggling with these problems. anything helps. thanks.
Best Answer
Double-check your calculator. You're calculating $\cos$ and $\sin$ using radians - you want to be using degrees. You'll learn the difference later on, but suffice it to say for now that radians and degrees are two different units by which angles are measured; a full rotation is $2\pi$ radians and also $360^\circ$.