SantosForgetsPassWds

Assuming a normal bath tub size plug or 3 square inches. The pressure at the bottom of the ocean is about 16,000 psi. Using Bernoulli's equation, the flow rate would be 330 m/s (roughly the speed of sound in air.) This gives a flow rate of about 0.6 m^3/s. Given the total volume of the Pacific Ocean (about 660,000,000 km^3), it would take 10 billion years assuming constant velocity. Since the pressure would decrease as the water level fell, it would actually take significantly longer.

I'm pretty sure this is one of my students. If so, then, dude, seriously? I have office hours. If not, the...

Work = ForceDistance = -kx² / 2

Woodchucks have a lifespan of about 5 years. At 2 m/s, a woodchuck would chuck about 300,000 km of wood in that time frame.

Wow...starting off with the hard ones. Surface tension is one of my weaker physics areas, but I'll give it a shot...

EDIT: This one's going to take me a bit longer. Will reply later.

EDIT 2: This took way longer than expected. I looked up a reference for stone skipping (which I expect has similar physics) and pulled an equation from there. Assuming a mass of 1.5 kg wheel, I get about 10 m/s (~22 mph).

Thank you, happy2x. That was a challenge.

SHAMELESS BOOK PLUG ALERT I did similar calculation in my book, Ballparking: Practical Math for Impractical Sports Questions.

Assuming they have the same density of air (1.2 kg/m^3), a volume of 10 cm^3, and come out in 1 second with a speed of 1 m/s, the net upward force up would be about 0.01 N. That's enough force to lift 0.002 pounds. To lift myself up, I'd need a net force capable of sustaining 180 pounds. This means I'd need to continuously sustain about 90,000 farts to propel myself upward.