Pulley + Projection Dynamics/Kinematics Q [Star Wars!]

jb182

I got this today as a take home bonus after a grade 12 physics test on kinematics and dynamics.

QUESTION: Han Solo is holding a rope that 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 zons 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.

Note: The picture has HAN standing next to his ship (its a 2D pic). There is a rope going perfectly horizontal to the edge of the 'cliff'. The cliff drops off perfectly vertical (ie. 90 degrees to the horizontal) and then after '5 zons' it levels off to the perfect horizontal (looks kinda like a stair on a stair case). Han is holding onto the rope which goes across the horizontal, drops off the edge of the cliff and its holding leia in the air 3 zons above the ground.

I've been trying for the last hour and a half to equate the equations and somehow cancel out the g values, but I can't get it. For simplicity, you can say alisons are kg, and zons are m.

Any help is appreciated! Thanks!

LowlyPion

Welcome to PF.

Maybe focus on how he is accelerated?

As a system until Leia hits the ground they are both accelerated by 55/135*G_a where G_a is the alien gravity in units/s²

They are accelerated for 3 units. That means that Hans will have a horizontal V² = 2*55/135*G_a*3 = 2.444 G_a

How long to fall the 5 units for Han then? Won't that time times his horizontal V be how far away he lands from Leia and her coiled bun hair-do?

lubuntu

I'd try introducing Jabba the Hut to the problem, should clear everything up.