A ferris wheel with a 40-ft diameter rotates once every 30 seconds. the bottom of the wheel is located 1.5 feet above the ground. you get on at the very bottom of the ferris wheel at time t = 0 and then the ferris wheel begins to turn counter-clockwise. for the problems below, assume the wheel makes 2 full rotations. a. at what times are you at the top of the ferris wheel? what is the height at the top of the ferris wheel?

b. at what times are you at the bottom of the ferris wheel? what is the height at the bottom of the ferris wheel?

c. at what times are you in the exact middle of the ferris wheel? what is the height of the exact middle of the ferris wheel?

d. write a cosine function to model your height above the ground over time, t.

Step-by-step explanation:

Let y = -A cos B(t -c) + D

A, amplitude = 20ft

Period = 2π / B ( B = π / 15)

= 30

c = 0

Vertical shift D = 21.5 ft

Equation becomes

a) Top of the ferris wheel is

t = 15sec, 45sec, height = 41.5ft

b) At the bottom of the ferris wheel

t = 0, 30sec, 60 sec

height = 1.5ft

c) Exact middle of the ferris wheel

t = 15/ 2 = 7.5sec, 22.5sec, 37.5sec, 52.5sec

d)

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕