Duke Caboom's Big Jump - Toy Story 4

Toy Story 4 is one of Pixar’s newest cinematic masterpieces, I’d say. It’s filled with adventure, rebellion, suspense, youthful innocence, the dream that toys can come alive, a love story, and, the best of all, a Canadian daredevil. Duke Caboom is one of the most charming, slightly egotistical, and ironically comical characters the movie has to offer. 
He's also a little self-deprecating but it makes for the big scene at the end of the movie I'll be analyzing. On a mission to save Bonnie, the toys' owner, and Forky, the newest member of the toy family, Duke Caboom takes a big risk and makes a big jump off the arm of a Ferris wheel.

In the scene, he hops off the center axis of the Ferris wheel on his bike, landing on one of the upward-moving arms. He then goes as fast as he can, reaching the end of the higher elevated platform and lifting himself off at the last second. The target he is aiming for is below him, though, making it a little easier to reach. According to the movie scene, the target is 40 feet away, but it looked a little farther than that so I estimated about 15 meters. Duke also leaves at a height that is approximately 9.5 meters from the target, and an angle of 22.5 degrees- 360 degrees divided by the 16 arms on the wheel. Of course, he makes the jump and sticks the landing, sort of. But how fast must he be going to make it?

By using a kinematic equation for both the x and y directions and substituting time in the y-equation with x-values, I was able to come up with an equation that would give me Duke Caboom's initial velocity. After plugging in all the values I knew, including distance, acceleration, and the angle at which the platform was at, his initial velocity came out to be 9.07m/s. This converts to about 20.3mph. To put that in perspective, the average cyclist can reach between 10 and 12 miles per hour. Most toy cars only move at approximately 1.5-3.5 mph. So, that must be one powerful bike Duke has. It also makes out that he has an air time of about 1.79 seconds, which makes sense if his tiny toy bike had enough horsepower to propel him at 20 miles an hour. It's hard to tell from the movie what his actual air time is though since this part of the scene is in slow motion. All in all, a very awe-striking scene, but not very convincing physics-wise.


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