Start of Questions A Ferris wheel is 30 meters in diameter and boarded from a pl

Question

Start of Questions A Ferris wheel is 30 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 27 meters above the ground?
Start of Questions A Ferris wheel is 30 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 27 meters above the ground?
Start of Questions A Ferris wheel is 30 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 27 meters above the ground?

Explanation / Answer

comparing with h(t)= Asin(B(t+C)) +k

k=3+(30/2) =18

A=(30/2) =15

period =10 minutes

=>2/B = 10

=>B=/5

h(t)= 15sin((/5)(t+C)) +18

six o'clock position on the Ferris wheel is level with the loading platform =>h(0)=3

15sin((/5)(0+C)) +18 =3

=> 15sin((/5)(C)) =-15

=>sin((/5)(C)) =-1

=>(/5)(C) =(-/2)

=>C =-(5/2)

equation of motion is h(t)= 15sin((/5)(t-(5/2))) +18

when ride is spent higher than 27 meters above the ground ,h(t)>27

=>15sin((/5)(t-(5/2))) +18>27

=>15sin((/5)(t-(5/2))) >9

=>sin((/5)(t-(5/2))) >(9/15)

=> sin-1(9/15)<(/5)(t-(5/2)) < -sin-1(9/15)

=> (5/)sin-1(9/15)<(t-(5/2)) < 5 - (5/)sin-1(9/15)

=> (5/2) +(5/)sin-1(9/15)<t< (5/2) +5 - (5/)sin-1(9/15)

time  spent higher than 27 meters above the ground= [(5/2) +5 - (5/)sin-1(9/15)]-[ (5/2) +(5/)sin-1(9/15)]

time  spent higher than 27 meters above the ground= 5 - (10/)sin-1(9/15)

time  spent higher than 27 meters above the ground= 5 - 2.0483276469913345164919784755052

time  spent higher than 27 meters above the ground= 2.952 minutes approximately

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