# Would a human achieve and surpass free fall speeds on a 11 km long, 9.5 km high, 60 degree angle water slide?

I`m wondering if it would be possible for a human of any body mass down a 11 km long, 9.5 km high, 60 degree angle water slide accelerate above the speeds they would reach at free fall from the same height?

What speeds (approximately) would they achieve on such a water slide at body mass of 80 kg by the time they reached the bottom of the slide?

## 1 Answer

To get the "terminal velocity", you simply equate the force of gravity to the force that is opposing it, often called either friction or air resistance. In the case of air resistance, the force is often proportional to the square of the velocity, and that's how you get a terminal velocity. Friction by itself tends to not depend on velocity much, so in principle you could get to very high speeds, but only if there were no air resistance. So the answer to your question is that it might be possible to get to very high speeds in an evacuated tube with a waterslide running down it, but not if there is air-- putting the tube at an angle only reduces the force of gravity, it will not reduce the force of air resistance and so you end up with a slower terminal speed if gravity is weaker. (To calculate the answer, you need to know the cross sectional area to get the air resistance, but if we assume air resistance is the same in both cases and is the dominant retarding force, we can say that a 60 degree angle reduces gravity by 1/2, so the terminal speed on the slide is lower by a factor of 1 over the square root of 2 compared to free fall, making standard assumptions.)

• My comment did not allow for air resistance, my apologies I deleted it, have a look at this related question: physics.stackexchange.com/questions/275847/… – user108787 Sep 11 '16 at 20:25
• It would seem unfair to compare a terminal speed in free-fall with air resistance, to one on a water slide without air resistance. – Ken G Sep 11 '16 at 21:23