A spinning ride at an amusement park is a wheel that has a radius of 21.5 feet and rotates 12 times per minute. A car on the ride starts at (21.5,0). What are the coordinates of the car's location after 6 seconds? Round to the nearest tenth.
So the car starts on the circumference? Good
So find the circumference first, we needa use that to determine how far along the thing he went.
21.5*2pi = 135.0884841043611093
I'm not gonna round till the end
12 rounds per minute, and a 6 second ride.
The ride makes a round every 5 seconds, so we needa add one round plus 1/5th a round to get
135.088 + 135.088(1/5) = 162.10618092523333116 - I shortened the equations after the calculation, so it wouldn't take up so much space. The calculations are completely accurate
So, he rode around for 162.10618092523333116 feet
Nevermind, I'm stupid. Just take 1/5th the round and then move him that far along the circumference to find the coordinates.
135.0884841043611093(1/5) = 27.01769682087222186
Now here is where I need CPhill.... I don't have any clue as to how to calculate coordinates on a circle.
The wheel completes 1 rotation in every 5 seconds...so...in 6 seconds.....it rotates another 1/5 times = (1/5) (360 degrees ) = 72 degrees [ using standard position]
So....the position after 6 seconds =
[r cos θ , r sin θ ] ......using r = 21.5 and 72° = θ, we have
[ 21.5cos(72) , 21.5 sin (72) ] = about [ 6.64 , 20.45 ]
Welp, I had no idea what I was talking about
Thank you so much!