A Ferris wheel of radius 100 feet is rotating at a constant angular speed ω rad/sec counterclockwise. Using a stopwatch, the rider finds it takes 4 seconds to go from the lowest point on the ride to a point Q, which is level with the top of a 44 ft pole. Assume the lowest point of the ride is 3 feet above ground level. Let q(t)=(x(t),y(t)) be the coordinates of the rider at time t seconds; i. e., the parametric equations. assuming the rider begins at the lowest point on the wheel, then the parametric equations will have the form: x(t)=rcos(ωt-ω/2) and y(t)=rsin(ωt -ω/2), where r,ω can be determined from the information given. provide answers below accurate to 3 decimal places. (note: we have imposed a coordinate system so that the center of the ferris wheel is the origin. there are other ways to impose coordinates, leading to different parametric equations.)

Find r, ω during the first revolution of the wheel, find the times when the rider's height above the ground is 80 feet.

First time t = 5.699 s

Second time t = 21.049 s

Step-by-step explanation:

Find the change in angle for 4 seconds.

cos(Δθ) = (100 + 3 - 44 ft) / (100 ft)

Δθ = 0.9397375 rad

Calculate ω.

ω = Δθ/Δt

ω = (0.9397375 rad) / (4 s)

ω = 0.2349 rad/s

Parametric equation for y:

y(t) = 3 ft + (100 ft) sin(0.0.2349t - π/2)

Find first 2 times for y = 80 ft.

80 = 103 + 100 sin(0.2349t - π/2)

-0.23 = sin(0.2349t - π/2)

-0.232078 + 2πn = 0.2349t - π/2 or (π + 0.232078) + 2πn = 0.2349t - π/2

First time:

-0.232078 = 0.2349t - π/2

1.338718 = 0.2349t

t = 5.699 s

Second time:

π + 0.232078 = 0.2349t - π/2

4.944467 = 0.2349t

t = 21.049 s

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have