Solutions due by noon on Friday, September 2.
If you watched Star Wars Episode IV – a New Hope, you remember that Leia, Han and Luke get trapped in a garbage chute. Let’s consider an similar garbage chute, a perfect cube. The chute crushes garbage by moving two opposite side walls towards each other. (As shown in the picture on the right, the walls on the left and right are moving toward each other.)
A fly gets trapped in this garbage chute, and rests peacefully on one of the crushing walls. Suddenly, the walls start to move, and the fly panics. It starts to fly perpendicular to one moving wall to the other. As soon as it reaches the other wall, it turns right back and flies in the opposite direction. In other words, it travels the shortest distance between the two moving walls.
The walls are stationary and 20 meters apart before they start to move towards each other. And they accelerate at 1 m/s2 toward each other, and stop moving when they come together (0 meter apart). The fly travels at 2 m/s, and continues to fly back and forth until it gets crushed by the walls. Assume that the fly can change direction instantaneously. What’s the total distance the fly travels before it meets its doom? Show all your work.
This problem is brought to you by Dr. Choong-Soo Lee.
Submit your solutions to Dr. Choong-Soo Lee. You may leave a hard copy in his mailbox or submit an electronic file via Dropbox. Good luck!
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