How fast you can drive your bike but not get wet?

[radoo]

You are wondering how fast you can drive your bike but not get your feet wet when the road is full of water?
The answer is simple: about 2.5m/s (meters per second) or roughly 9km/h (kilometers per hour), or 5.6mph. See below for the demonstation:
This is a simple physics problem which is solved using the law of conservation of energy. The more interesting fact is that your speed will not depend at all on the mass of the water drop that flies off the spinning wheel. The key to the solution is considering that the drop will fly off with the speed of your wheel which is, in fact, the speed indicated by your speedometer. So, in your reference frame the drop flies from zero ground when it has maximum velocity to, say 30cm when it has no velocity at all. This means that the mass of the droplet x(multiplied by) height 30cm x gravitational constant(approx 10) must equal the mass of the droplet (again!) multiplied by the square of the velocity over two. This law states that the potential energy must equal the kinetic energy of the drop, and more, that the initial kinetic energy of the droplet transforms into the potential energy at the level of your feet. Dividing each sides of the equation by the mass of the droplet we obtain that the velocity does not depend on this mass. So, there you have it: v=square root of 2*10*height which yields about 2.5m/s. So we learn from elementary physics that you must not drive faster than this speed if you don't want to get wet:)

 

[mfb]

Two issues I can see:

• the tire can lift the water droplet above the ground before it gets in free fall.
• there are other ways you can get wet, not only drops falling off the tire.

 

[tkjtkj]

As the question is stated, you can drive as fast or as slowly as you wish , on a dry day ...

Solving problems requires that the real problem be recognized and clearly stated .. which I feel has not been done in the instance ... Care to be more-specific ?

 

[sophiecentaur]

Probably a bit too 'ideal' a model. Surface tension must be relevant here. But you could imagine an equivalent scenario with balls in cups on a wheel and the result would be a bit more realistic, I think.
A similar idea but the other way round is to calculate what g force acts on a fairground swing boat when released from horizontal. It's also independent of the radius.