Question

Trigonometry Story Problem? A gondola on an amusement park ride spins at speed of 13 revolutions per minute. If the gondola is 25 feet from the ride's center, what is the linear speed of the gondola in miles per hour. (Hint: 5280 feet=1 minute).

Answer 1

23.2 mph What you do is figure out how far the gondola is moving. Given that it's moving in a circle with a radius of 25 feet, the circumference is: 2 * 3.14159 * 25 = 157.08 feet. Now it travels that distance 13 times per minute giving: 157.08 * 13 = 2042.04 feet per minute. Finally, assuming it keeps up that speed for 1 hour, you get 2042.04 * 60 = 122522.4 feet per hour. Now convert that to miles per hour by dividing by 5280 122522.4 / 5280 = 23.2