Solve The Gobbling Gorilla Puzzle

[peteb]

A puzzle with no tricks or "gotcha"s, just the laws of physics:

A gorilla, of mass 100kg, is imprisoned inside a cage of mass 350kg, which is suspended in mid-air on a long rope thrown over a pulley. At the other end of the rope is a counterweight of mass 450kg, exactly balancing the combined weight of the cage and gorilla.

Attached to the roof of the cage, on the inside, is a delicious bunch of bananas, which the gorilla would love to eat. Unfortunately they're out of his reach, by 10cm. He decides to jump up into the air, just far enough to be able to grab the bananas, then fall back down to the cage floor. Assume that the pulley is frictionless, and that the masses of the pulley and rope are negligible compared to the gorilla and cage.

How fast does he need to jump? Specifically, with what speed does the gorilla need to move away from the cage floor? Show how you calculated your answer.

Have fun----

Pete B

 

[BobG]

Spoiler

Whose reference frame? Relative to the cage, the gorilla has to be going 1.4 meters per second and pushes off with the same force as if he were on solid ground. The difference between the gorilla's velocity and the cage's velocity has to be 1.4 meters per second (equations for projectile motion). The gorilla's momentum (mv) has to be equal to the cage's momentum, so the gorilla must start out with an upwards velocity of 1.24 meters/sec while the cage has a downward velocity of .155 meters/second, which is close enough for slide rule accuracy.

 

[peteb]

That was quick!

Pete B