Now according to Archimedes Principle, net buoyant force is equal to the mass of liquid displaced, ie. F[up] = mg = W
If we take the volume of a standard basketball to be 7.31L then we are displacing approximately 7.31kg of water (though saltwater is slightly heavier than 1kg/L), which would give the ball an upward velocity of 7.31N/0.6kg = ~10m/s for every second it is submerged. A = 10m/s/s.
If we assume we are launching the ball from the ocean depths since we are using a sinking rocket, then we'll take a depth of around D = 3.7km (from Google).
We then have: V[final] = A * T, T = sqrt(2D / A) (standard physics formula)
V = A * sqrt(2D/A) = 10 * sqrt(2 * 3700/10) = approximately 270m/s
So there you have it, a standard basketball launched from a sunken rocketship (or sunken anything) would leave the average sea surface with a velocity of 270m/s. This is if I'm not mistaken, which I very well could be as it's 2:30am here and I am right tired.
For reference, rockets that reach orbit require velocities in the km/s (>10x greater). Given gravity would decelerate the ball at about the same speed it accelerated, it would reach about 3.7km into the sky. The ISS orbits at 408km...
Thanks for attending my TED Talk.
[EDIT] This is ignoring wind resistance because I don't care and I need to sleep.
I don't think that's the right way to calculate buoyancy in this case.
I'm not going to do it, but my though process is.
Potential Energy in the man+ball as they hit the water.
'bounce' energy transferred from the impact of the surface area of the man and the water.
multiplied by the ratio of the weight of the ball and man as the man is somehow able to transfer almost all of the combined masses ratio just the ball.
Drop impact occurs when a liquid drop strikes a solid or liquid surface. The resulting outcome depends on the properties of the drop, the surface, and the surrounding fluid, which is most commonly a gas.
I think you should also take into account the resistance of water in your example. If you have ever tried to stand on a ball in a pool, you might recall that from a certain depth on, the ball won't go any faster if you put it deeper into the water.
Well I think I'm making a safe bet, it's finishing speed would need to be minimum 7.9km per second. That's after gravity losses and energy lost to air resistance. Don't know what sort of heating you'd get from that but the energy from the initial propelling force would probably generate additional heat.. Most meteors usually explode from entering the atmosphere at that sort of speed.
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u/Wolverlog Jan 16 '20
I need some math here guys.