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# Rotations

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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.

Apr 19, 2016

#1
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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.

Apr 19, 2016
#2
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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 ]   Apr 19, 2016
#3
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