Question

Preston and Odina are riding the Prince Charming Carousel at Disney World. Preston is on a horse feet from the center. Odina is on a horse feet from the center. Prince Charming has the carousel spinning at revolutions per minute. What is Preston's linear speed (in feet per second)?   ft/sec What is Odina's linear speed (in feet per second)?   ft/sec

Answer 1

Preston's linear speed is 10π ft/sec and Odina's linear speed is 12π ft/sec.

Step-by-step explanation:

To find Preston's linear speed, we need to convert the given information about the carousel's revolution per minute. We can use the formula:

V = 2πrN

where V is the linear speed, π is pi (approximately 3.14), r is the radius from the center, and N is the number of revolutions per minute.

For Preston, his radius from the center is given as feet. Plugging in the values, we have:

V = 2π(10)(3)

V = 60π ft/min

To convert this into feet per second, we divide by 60:

V = 60π/60 = 10π ft/sec

Therefore, Preston's linear speed is 10π ft/sec.

To find Odina's linear speed, we use the same formula but change the radius to feet:

V = 2π(12)(3)

V = 72π ft/min

Converting this to feet per second, we have:

V = 72π/60 = 12π ft/sec

Therefore, Odina's linear speed is 12π ft/sec.