Chapter 4.8, Problem 34E

Solution

To find: The equation that models the height of a rider who begins at the bottom of the wheel when $t=0$

  $h=25\sin \left(\frac{\pi t}{10}+\frac{3\pi }{2}\right)+33$

Given information:

Given, for the given Ferris Wheel below, an equation models the height of a rider who begins the ride at the bottom of the wheel when $t=0$ .

  

The given options are:

  $h=25\sin \frac{\pi t}{10}$

  $h=25\sin \frac{\pi t}{10}+8$

  $h=25\sin \frac{\pi t}{10}+33$

  $h=25\sin \left(\frac{\pi t}{10}+\frac{3\pi }{2}\right)+33$

Calculation:

Checking the options:

a. Here, at $t=0$ , $h=0$

And the height changes between -25 and +25.

Hence this option is not correct.

b. Here, at $t=0$ , $h=8$

And the height changes between -17 and +33.

Hence this option is also incorrect.

c. Here, at $t=0$ , $h=33$

And the height changes between 8 and 33.

Since the rider starts at the bottom, the height cannot be 33 when $t=0$ .

d. Here, at $t=0$ , $h=8$

And the height changes between 8 and 33.

Hence option d is the required equation.

Conclusion:

  $h=25\sin \left(\frac{\pi t}{10}+\frac{3\pi }{2}\right)+33$