Wednesday, May 7, 2025

SIN Bin: 1999, Problem 2

By Department Faculty

Problem

Diagram of Han Solo holding on to his ship on supporting Lea, who is hanging on by a rope over a cliff. The height of the cliff and Lea above the ground are shown.

Han Solo is holding a rope which is supporting Princess Leia, of mass 55 alistones (an alien unit of mass), 3 zons (an alien unit of length) above the ground as shown. Han, of mass 80 alistones, is holding onto his spaceship, the Millennium Falcon, standing on the frictionless surface of an alien cliff, and he is more than 3 zons from the edge. When he loses his grip on the ship, both he and the princess accelerate to the same speed until she lands on the ground, at which point she releases the rope. Soon after, Han will fall off the 5 zon high cliff as a projectile. How far from the princess in zons does he land on the level surface? The gravitational acceleration on this rebel planet is unknown.

  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Solution SIN Bin: 1999, Problem 2

(b) 5 zons (4.94 zons)

Han Solo and Princess Leia act as a single mass as far as acceleration over the cliff is concerned, but the force driving them comes only from Leia's weight. Thus their common acceleration is:

a = MLeia * g / (MLeia+ Msolo) = 0.407g, and in a fall of height h (3 zons) the final velocity vf becomes sqrt(4ahh0 / g) = 4.94 zons from Leia. Fortunately gravity cancels out (since a is proportional to g), leaving only mass rations and the alien unit of distance, the zon. A problem cast in an alien setting tends to scare many people, less than half of the students tried this problem!