Question

40 POINTS QUESTION

PLS HELP

A Ferris wheel with a radius of 19m rotates once every 56 seconds. The top of the
wheel is 42.5m above the ground.

Determine a sine and cosine equation of the function that gives the rider's height
above the ground in metres, as a function of time, in seconds, with the rider starting
at the bottom.​

Answer 1

(First of all its 20 points not 40 but any ways) A ferris wheel has a raidus of 20 m. Passengers get on halfway up on the right side. The direction of rotation is counter clockwise. The bottom of the ferris wheel is 2 m above ground. It rotates every 36 seconds. Determine height above the ground after 15 seconds algebraically. Determine seconds to the nearest tenth when height is 38 m above the ground algebraically.

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let t=seconds after wheel starts to rotate.

let h=meters above ground after wheel starts to rotate

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The formula I got: h(t)=20sin(πt/18)+22

This is close to the formula you got, except I left the negative sign out since passengers start to rise after the wheel starts going counter-clockwise.

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After 15 seconds:

h=20sin(15π/18)+22

=20sin(5π/6)+22

=20*(1/2)+22

=32 m

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When h=38 m

38=20sin(πt/18)+22

38-22=20sin(πt/18)

20sin(πt/18)=16

sin(πt/18)=16/20=4/5=.8

arcsin(.8)=0.927

πt/18=0.927 (radians)

t=(.927*18)/π≈5.31

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height above the ground after 15 seconds≈38 m

seconds elapsed when height is 38 m above ground≈5.3 seconds