Grades skipto9 nMath Horne i My Classes Help l Log Out Alys

Grades! × skip&to-9; nMath Horne i My Classes Help l Log Out Alysha Souba Due Tue 12/12/2017 6:00 am A Ferris wheel is 20 meters in diameter and boarded from a platform that is S meters above the ground. wheel completes 1 full revolution in 8 minutes. How many minutes of the ride are spent higher than 24 meters above the ground? The six o\'clock position on the Ferris wheel is level with the loading platform. The Points possible: 4 This is attempt 1 of 10.

Solution

period ,2_/B =8 minutes

=>B=_/4

diameter =20 meters

amplitude ,A=20_/2

=>A=10

height of midline above the ground , D=(20_/2)+5

=>D=15

so the equation of motion is y=-10cos((_/4)t) +15

in the first revolution. 0t8

=>0(_/4)t2

for the time of ride spent higher that 24 meters above the ground

-10cos((_/4)t) +15 >24

=>10cos((_/4)t) -15<-24

=>10cos((_/4)t) <-9

=>cos((_/4)t) <-9_/10

=>-cos^-1(9_/10)< ((_/4)t)<+cos^-1(9_/10)

=>4-(4_/)cos^-1(9_/10)< t<4+(4_/)cos^-1(9_/10)

time spent 24meters above ground =(4+(4_/)cos^-1(9_/10))-(4-(4_/)cos^-1(9_/10))

time spent 24meters above ground =(8_/)cos^-1(9_/10)

time spent 24meters above ground =1.14853 minutes approximately