Ferris Wheel Height Function: Diameter, Location, and Time Analysis

[yourmom98]

The height (in metres) of a rider on a ferris wheel after t minutes can be described by the function y=67sin[(pi/15)x -30]+70

a) what is the diameter
b) where is the rider at x=0? explain the significance
c)how high off the ground is the rider at the top of the wheel?
d) at what times will the rider be at the bottom of the ferris wheel?
e) how long does it take for the ferris wheel to go through one rotation

a) 134 meters
b) i graphed this and found the y value for when x=0 and it was not at the bottom of the graph what does this mean? if time/x is zero shouldn't they rider be at the bottom?
c)137 meters
d)15.7436 (from graphing) is there a way to solve this without graphing?
e)30 min

can you check my answers can help me with b) and d)

 

[mezarashi]

The height (in metres) of a rider on a ferris wheel after t minutes can be described by the function y=67sin[(pi/15)x -30]+70

a) what is the diameter
b) where is the rider at x=0? explain the significance
c)how high off the ground is the rider at the top of the wheel?
d) at what times will the rider be at the bottom of the ferris wheel?
e) how long does it take for the ferris wheel to go through one rotation

a) The maximum value of sin(anything) = 1. The minimum of sin(anything)=-1. Take the maximum height - minimum height, you will get diameter. Does this also help answer something about the (+ 70) at the end?

b) time = 0 seconds, doesn't mean that they should be at the bottom. What if I started this equation when the ride was half way through.

c) ^_^

d) The rider will be at the bottom of the ride whenever the graph is at it's lowest. The minimum of sin(anything)=-1, thus 3 is the lowest you can get. Equate the equation to 3. It will be periodical of course, so add in the period of the ferris wheel's full turn.

e) I see you have the answer ready for part (d) ;)

 

[yourmom98]

i don't understand what you said for d) 70 is not the lowest point on the ride the lowest point on the ride is 3m you can see this from the graph. because since the sine function was stretched by a factor of 67 raising it up 70 units would only put the minimum at 3 meters because amplitude is 67 also for a) you can just do 2 times a value 2*67=134 (this is correct) to get the same answeras max-min

 

[mezarashi]

You are right. I've corrected my complete blunder in simple mathematics :P
See above again. Sorry about that.