Question

Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.

Answer 1

The distance from the bottom of the wheel to a point on the ground can be modeled by a sine function. h(t)=a*sin(kt)+b. b is the height of the wheel, or 4m. a is the radius of the wheel, 50/2=25m. 2pi/k is the 5sinof thw revolution, so 2pi/k=6/3=2, k=pi. h(t)=25sin(pi*t)+4. 

Answer 2

Answer:

The required function is $h(t)=-25\cos(\pi t)+29$.

Step-by-step explanation:

The general form of cosine function is

$y=A\cos(Bt+C)+D$

where, A is amplitude, $\frac{2\pi}{B}$ is period, C is phase shift and D is midline.

It is given that the Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. So the minimum value of the function is 4 and maximum value is 50+4=54.

$D=\frac{Maximum+Minimum}{2}=\frac{54+4}{2}=29$

It takes six minutes to do three revolutions on the Ferris wheel. So, period of the function is

$period=\frac{6}{3}$

$period=2$

The period of a cosine function is

$\frac{2\pi}{B}=2\Rightarrow B=\pi$

The function have no phase shift. So, C=0.

Substitute y=h(t), B=π, C=0 and D=29 in equation (1) to find the function.

$h(t)=A\cos(\pi t+0)+29$

It is given that the ride is at the low point whet t=0, it means the function passes through the point (0,4).

Substitute t=0 and h(t)=4 in the above function.

$4=A\cos(\pi (0)+0)+29$

$4=A+29$

Subtract 29 from both the sides.

$4-29=A+29-29$

$-25=A$

The amplitude of the function is -25.

Substitute y=h(t), A=-25 B=π, C=0 and D=29 in equation (1) to find the function.

$h(t)=-25\cos(\pi t)+29$

Therefore the required function is $h(t)=-25\cos(\pi t)+29$.