You and your team have been hired by Marvel Entertainment to develop a stunt for the next offering in the Marvel Cinematic Universe – Black Panther. This film introduces a new character: T'Challa, the Black Panther.

In a scene meant to take place in T'Challa's homeland of Wakanda, a young T'Challa (played by Jaden Smith) is searching for vibranium (Wakanda's chief export) on a large hill. While digging, he disturbs a large boulder, which begins to roll down the hill after him. In the scene, T'Challa is meant to sprint down the mountain while the boulder rolls behind him, catching up, but not running over T'Challa.

The production studio has designed several boulders (some solid spheres, some hollow spheres, and some cylindrical ones) for the stunt, but doesn't want to manufacture and ship all of them to the set. Also, they have yet to choose a stunt person because they aren't sure how fast that person will need to run down the hill. They've asked your team to design the stunt including the hill and to produce a graph that demonstrates how the speed of the boulder will change as it rolls down the hill. It's foam, but it's big.

Remember this is Hollywood, so make sure the stunt is exciting!

Learning Goals Week 10

Your success with the previous stunt has lead to your being hired by Marvel Entertainment again for the new Avengers - Infinity War movie. Benedict Cumberbatch appears again as Doctor Stephen Vincent Strange, a neurosurgeon who protects the Earth from magical threats both foreign and domestic.

In one of the final scenes of the movie, Doctor Strange has been captured by Nightmare and has been sent to the Dark Dimension using a teleportation system constructed by Dormammu. The teleportation system is located on a small island above the Arctic circle. Ms. Marvel and Spiderman arrive to save Doctor Strange by crossing into the Dark Dimension. They find a sled that can be used to launch them into the teleportation system. Spidey uses his web shooters to attach a web strand to the teleportation system and accelerate he and Ms. Marvel into the teleportation system.

For this stunt, the current plan is to use a sled ($M_{\rm sled} = 1500\,{\rm kg}$) with a wire reel system attached to the front end. The wire will be attached to a snowmobile and the sled will be dragged across the ice while the wire unwinds from the reel. The sled must be traveling with a speed of 30 m/s at a distance of 100 m from its starting location.

Unfortunately, the island was chosen for its beauty and not any sort of safety considerations. The island itself is only 2.5 km across at its widest point, so the wire cannot unwind too much or the snowmobile will end up in the frozen arctic waters.

The reel is hoop-shaped, but its mass has not been chosen. Your team is meant to decide how to proceed with the stunt, and report back to the production company. Find the appropriate force that the snowmobile should exert on the wire/sled, and determine the mass of the reel. Some initial testing of reels of different masses and radii have shown (for a constant force) that the relationship between the angular speed of the reel and the linear speed of the sled is related to the ratio of the masses of the sled and reel. The equation that best fits this data is given below,

$$\omega_{reel} = \dfrac{M_{sled}}{m_{reel}}\dfrac{v_{sled}}{R_{reel}}$$

Learning Goals Week 10