How Do You Calculate the Speed of a Water-Tube Towed by a Boat?

[Varano]

Hey everyone, I am having trouble finding out the equation I need. Could someone please walk me through finding out the Speed of a Water-Tube if it is being whipped behind a boat on a 75ft rope, and the boat is traveling at a speed of 60mph? Any help would be greatly appreciated, I've been struggling with this problem for a while now.

Sincerely -
Varano

 

[Doc Al]

Can you describe the problem in a bit more detail? What's a "Water-Tube"?

Whatever it is, if it's being dragged by a stiff rope in a straight line by a boat going 60 mph, then it had better be moving at the same speed in that direction, don't you think? I suspect there's more to it.

 

[Varano]

HaHa, sorry about that, a water tube is one of those inflatable donuts that you attach to the back of a boat and people ride on them in the water. And yes, the tube would be going the same speed as the boat, but when the boat turns, I think centripetal force applies to the scenario and the tube begins to travel a lot faster than the boat in order to keep up with it.

I am certain that what I'm looking for requires the speed of the boat, and the length of the rope. It possibly requires the tension of the rope which would be at maximum tension, perhaps 100 N, I'm not to sure about that though.

 

[denverdoc]

this is likely not a problem for the wee hours, but having a little insomnia. And it beats worrying about taxes. But beware I have never water tubed.

First, until Doc Al, shows me what a fool I am in the morning, i think your premise is right, that the speed can exceed that of the boat. For me the most intuitive approach was to consider the boat moving in a line and being able to swerve back and forth like a water skiier--I believe this is fair but rotating inertial frames of reference is not a subject I have studied.

It would seem that as one skis from the center to one side in an arc, they gain ground on the boat in the terms of Y displacement. Not only that but they have managed to achieve displacement in the x direction.

Then what struck me was a similarity in some respects to a moving pendulum. I got sidetracked into an even more interesting problem of an accelerating pendulum, but thought I'd at least pass these notions along in the hope it might help.