The Physics Behind Carnival Rides

A ride known as "The Paratrooper" is a must have at every carnival. The Paratrooper is, as pictured below, the ride that sends its riders spinning through the air. The Paratrooper often has 10 seats that stem out from its center at consistent angle intervals, forming a circle. These seats are supported by arms connected to the center of the ride. When the ride starts, the machine lifts the seats and their occupants high into the air and begins rotating, slowly amassing speed until it reaches its maximum velocity. At this point, the machine begins to tilt so that its riders are no longer perpendicular with the ground.

Understandably, this ride causes great thrill for those that ride it. However, what many of these riders fail to realize and appreciate are the aspects of physics that occur during this ride and enable it to be the ride that it is. During the short half a minute to minute ride, riders experience centrifugal force and gravitational pull, as well as the ride's velocity and acceleration.

On July 31, 1979 at a Canadian amusement park, one of these rides malfunctioned and a seat came loose, sending it and its occupants flying through the air. With the assumption that, at its maximum speed, the ride is spinning at 20 miles per hour, and that the riders were 10.668 meters in the air at the time that their seat came loose, how far did they travel through the air. Moreover, if the length of one of the ride's arms is 5.33 meters long, how much centrifugal force are the riders experiencing?

A rider of the Paratrooper experiences a centrifugal force of 14.995 m/s^2. Moreover, at the spend of 20 miles per hour, those unfortunate riders would have traveled through the air, 13.1865 meters away.

Work:
20 mph = 32186.9 meters per hour
32186.9 / 3600 = 8.94 meters per second

Ac = V^2 / r
Ac = 8.94^2 / 5.33
Ac = 14.995 m/s^2

delta(y) = Vi(t) + 1/2At^2
-10.668 = 0(t) + 1/2(-9.8)t^2
-10.668 = -4.9t^2
-10.668 / -4.9 = t^2
2.177 = t^2
t = 1.475 seconds

delta(x) = V(t)
delta(x) = 8.94(1.475)
delta(x) = 13.1865 meters

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