Question

a ferris wheel with a radius of 30 feet is rotating at a rate of 2 revolutions per minute at time t=0 a chair on the ferris wheel is at the lowest point which is 10 feet above the ground which of the following models describes the height h in feet of the chair as a function of time t in seconds​

Answer 1

Answer:

h=-30cos(pi/15t)+40

Answer 2

Answer:

The required equation is $f(t)=-30\cos(\frac{\pi}{15} t)+40$.

Step-by-step explanation:

The general form of cosine function is

$f(t)=A\cos(Bt+C)+D$             .... (1)

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

It is given that the radius of a ferris wheel is 30 feet. It is rotating at a rate of 2 revolutions per minute at time t=0 a chair on the ferris wheel is at the lowest point which is 10 feet above the ground.

It means the minimum value is 10 and maximum value is 10+2(30)=70.

Midline of the function is

$D=\frac{Maximum+Minimum}{2}=\frac{70+10}{2}=40$

1 min = 60 seconds

Period of the function is 2.

$\frac{2\pi}{B}=\frac{60}{2}$

$\frac{2\pi}{B}=30$

$B=\frac{\pi}{15}$

Phase shift is not given, so C=0.

Substitute $B=\frac{\pi}{15}\pi$, C=0 and D=40 in equation (1).

$f(t)=A\cos(\frac{\pi}{15}i t+0)+40$

$f(t)=A\cos(\frac{\pi}{15}i t)+40$       .... (2)

It is given that the graph passes through the point (0,10).

$10=A\cos(0)+40$

$10=A(1)+40$

$10-40=A$

$-30=A$

The value of A is -30. Substitute A=-30 in equation (2).

$f(t)=-30\cos(\frac{\pi}{15} t)+40$

Therefore the required equation is $f(t)=-30\cos(\frac{\pi}{15} t)+40$.