Question

So, I have a small idea of where I want to go with this problem: A car travels on a circular path with a radius of 41 meters. If the car travels at a distance of 214 meters, through what angle (in radians) does the car move?

Answer 1

I really wish I could draw this out. So, I have a hint here that tells me that the angle is equal to the ratio of the length measured along the arc and divided by the radius.

Answer 2

So I know that I have the radius. But the thing is, i have no idea what "s" or length is. They give me the distance that the car travels around the track but I have no idea how to use it.

Answer 3

The entire circumference of the track is 2(pi)(radius) = 257.5 m.
If you go around the entire track once, that is 360 o or 2 pi radians.

Here you have gone around the fraction (214/257.5)=0.83 or 83% of the circumference. That means you have gone 0.83(2 pi) radians in angle.

angle theta = (2 pi) (distance)/(circumference)

Answer 4

Ah okay okay, I understand now. Thank you so much. I appreciate it.

Answer 5

Glad to have helped.