I'm having a bit of trouble with this particular problem can some 1 please explain it to me?

Question

im trying to solve this problem but i just dont get it i been trying for hours but still nothing, well here it is:

A ferris wheel has a diameter of 70 feet, and the center is 38 feet off the ground. Eight seats are evenly spaced around the circumference. the entire wheel rotates counter clockwise once every 60 seconds. Assume your riding in the bottom seat (or in other words the one closes to the ground)

a) If the ride last for 3 minutes, draw a graph that records your distance from the ground every 5 seconds for the lenght of the ride.

b) If the ride last for 3 minutes, draw a graph that records your distance to the left or right as measured form the center of the ferris wheel every 5 seconds for the duration of the ride.

c)how high off the ground are u in 2 minutes 22.5 second of the ground

d) how far are u to the left or to the right 1 minute 7.5 second into the ride

You dont have to answer all of them if you cant, but i appreciate all the help you can give me .

Answer 1

Let
x – your distance to the right
y – your distance from the ground
h – distance of the center of the wheel from the ground
r – radius of the wheel
ω – angular speed of the wheel
t - time

The following equations are valid
x = h + r*sin(ω*t)
y = r*sin(ω*t – π/2)

In our case
h = 38 feet
r = 35 feet
ω = 2*π/min

a) See the blue graph here:
http://s210.photobucket.com/albums/bb64/oregfiu/?action=view¤t=ferris_wheel.jpg

b) See the red graph in the same picture.

c) y = 38 + 35*sin(2*π*22.5/60 – π/2) = 62.75 feet

d) x = 35*sin(2*π*7.5/60) = 24.75 feet to the right

-

Answer 2

Hi,

For the general form of this equation, we will use y = A cos(Bx + C) + D, where A is the amplitude, B is the normal period divided by the new period, C is the horizontal phase shift, and D is the vertical shift.

Since the diameter is 70 feet, then the radius is 35 feet, which will be used for A. Usually the cosine graph starts at its highest point, but our graph will start at the bottom, so we will change the amplitude from 35 to -35 to flip the graph over to start at the bottom.

A complete circle is 360°, but since it is covered in 60 seconds, then B = 360/60 = 6.

There is no horizontal phase shift, so C = 0 and drops out of the equation.

D is the vertical phase shift which is 38 feet, the distance off the ground to the center.

So the equation for the movement of a seat on the ferris wheel is y = -35cos(6x) + 38, where x is the time in seconds after the ride has started. Y will be the vertical height at x seconds.

Since the horizontal distance away from the center line can be found by using the Pythagorean Theorem as √(35² - (35cos(6x))²). For the first 30 seconds of each minute, the seat is to the right of center and the second 30 seconds of each minute would be to the left of center.

I used these equations in my TI83 for these answers:

y1 = -35cos(6x) + 38
y2 = √((35²-(35cos(6x))²))

a) That means the graph starts at a low point at 0 seconds, goes up to a max at 30 seconds and back down at 60 seconds. Then the graph goes from its low point at 60 seconds up to a max at 90 seconds and back down at 120 seconds. Then the graph goes from its low point at 120 seconds up to a max at 150 seconds and back down at 180 seconds.

b) Here are seconds, y and x distances. y distances are measured from the ground. x distances are to the right or left of the center line of the ferris wheel.
sec....y.....x
-----------------
..0...3.......0
..5..7.69..17.5
.10.20.5..30.31
.15.38......35
.20.55.5...30.31
.25.68.31.17.5
.30.73.........0
.35..68.31.-17.5
.40..55.5...-30.31
.45..38......-35
.50..20.5...-30.31
.55..7.69...-17.5
.60..0..........0
This same pattern repeats from 60 to 120 seconds and again from 120 to 180 seconds.

c) 2 minutes 22.5 seconds is 142.5 seconds. If x = 142.5 then y = 62.749 feet off the ground and 24.749 feet to the right of center.

d) 1 minute 7.5 seconds is 67.5 seconds. If x = 67.5 then 13.251 feet off the ground and 24.749 feet to the right of the center line of the ferris wheel.

I hope that helps!! :-)

Answer 3

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