Ferris Wheel problem, please help.

Question

A Ferris wheel with a radius of 15 m rotates once every 100 s. Riders board the Ferris wheel using a platform 1 m above the ground.

a) Draw the graph for two rotations of the Ferris wheel

b) Write an equation that gives the height of the rider as a function of time

c) Calculate the height of the rider after 2 min of the Ferris wheel. Round to 2 decimal places

Any help would be greatly appreciated, thank you.

Answer 1

general equation is

h(t) =AsinB(t+C)+D

where

A=amplitude =15

B= 2pi/period = 360(2)/period

= 720)/100= 7.2

C = phase shift

D = midline = 16

h(0) = 1 = 15sin7.2(t+C)+16

sin7.2C =-1

7.2C = 270

C = 270/7.2 = 37.5

h(t) = 15sin7.2(t+37.5)+16

is the equation for height after t seconds

h(0) = 15sin7.2(0+37.5) +16

= 15sin(7.2(37.5)) + 16

= 15(-1)+16=1

h(120) = 15sin7.2(120+37.5) +16

=15sin7.2(157.5) +16

=15sin1134+ 16

= 15sin(1134-3(360)) +16

= 15sin54 +16

= 28.14 feet high after 2 minutes

You could also do the equation in terms of cosine

but with a different phase shift, a different value

of C