## Related questions with answers

Carlos is the last person to board a Ferris wheel that has a radius of 52 feet. The counterclockwise arc swept out by Carlos is measured from where he got on, at the bottom of the Ferris wheel. Since Carlos is the last one to board, the Ferris wheel starts up and doesn't stop again unit the ride is over. a. Draw a diagram that show's Carlos's location and the angle swept out by Carlos at an arbitrary moment in time. b. Define a function f that relates Carlos's vertical distance above the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos. Over what interval of input will Carlos complete one revolution? c. Define a function g that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos Over what interval of input will Carlos complete one revolution? d. Suppose Carlos's cart is traveling 0.3 radii per second on a circular path as the wheel rotates. Define a function h that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? e. Marilyn claimed that she saw Carlos's cart travel at a speed of 3.5 radii per second. Is that possible? Explain. (Hint: Determine the cart's speed in miles per hour. f. Suppose that Carlos's cart traveled at 0.4 radii per second. Define a function j that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? g. Suppose Carlos's cart is traveling 0.2 radii per second. Define a function k that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? h. Sketch a graph of each function defined in parts (d)-(g). Label your axes. Identify the interval of input over which Carlos completes one revolution.

Solution

VerifiedWe know that Carlos is the last one to board the Ferris wheel with the radius:

$r=52~\text{ft}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Precalculus Pathways to Calculus: A Problem Solving Approach, Student Workbook

6th Edition•ISBN: 9780738085524Kevin Moore, Marilyn Carlson, Michael Oehrtman## More related questions

- computer science
- computer science

1/4

- computer science
- computer science

1/7