at a rate of .4 rad/sec, time taken for one rotation
= 2π/.4 seconds = appr 15.7 sec
amplitude = 8
for period: 2π/k = 15.70796..... , k = .4
starting equation: height = 8cos (.4t)
as it stands, the minimum is -8, we want it to be +2, let's flip it
so ... height = -8cos(.4t) + 10
check for some critical values:
t = 0, height = 2 , that's good
t = 15.708/4 , height = 10 , quarter way up, that's right
t = 15.708/2 , height = 18 , all the way up, correct
...
so when height = 14
-8cos(.4t) + 10 = 14
-8cos(.4t) = 4
-cos(.4t) = .5
cos (.4t) = -.5
I know cos 2π/3 = -.5
.4t = 2π/3
t = 5.23 seconds
You can check this by entering my equation into a webpage like
www.desmos.com/calculator
and checking the values
A Ferris wheel of diameter 16 m rotates at a rate of 0.4 rad/s and is lifted 2m off the ground. If a platform is made so passengers can board at the centre height of the ferris wheel as it goes up,
a) Determine the amount of time it takes to complete one full rotation
b) Determine a cosine function that models the height, h in meters, of the car relative to the ground as a function time, t, in seconds.
c) How long does it take the passenger to reach 14m above the ground for the first time if they started in the middle? Round answer to the nearest tenth of a meter.
2 answers
Hi, i think you equation may have a problem as since it is a cosine function and not a sine function, the d value can't be zero
1 answer