1. Jan 2, 2004

### craptacular

I'm at my wit's end trying to solve this question and I'm out of luck. Please help or suggest ideas. I have tried looking for similar problems in texts that are available but I keep arriving at the same answer I worked out which does not agree with the key's. Here's how the problem goes:

A motor boat is towing 2 skiers. At a particular moment, the boat exerts a force of 457 N on the 1st skier and a force of 525 Newtons East 30 degrees South on the 2nd skier. If the boat is moving at a CONSTANT velocity and the drag of friction is 325 Newtons, find the force that propels the boat [Answer: 1274 East 16 degrees South]

2. Jan 2, 2004

### Loren Booda

Is the drag of 325 Newtons for the boat? Is friction here considered proportional to velocity? What is the orientation of force for the 1st skier?

3. Jan 2, 2004

### fffbone

As you are dealing with vectors, it is essential to know both the magnitude and the direction. Since the problem did not clearly state the directions of forces, it is impossible to solve. But, in any case the force that "propels" a subject that has CONSTANT velocity would be zero, as the subject is not in acceleration. However, I think what the problem is trying to ask is that: what is the reaction force of all the forces mentioned above. And the answer to that would be the inverse vector of the resultant resistance(the resultant force of draging the two skiers and the friction in this case). You can now find the answer using basic trigonometric calculations(assuming you know both the magnitude and the direction of the forces of course).

4. Jan 2, 2004

### craptacular

oooops, yes the orientation of skier 2!

First, thanks for responding. I think I agree with the questions you're asking me, too, but if you're asking the same questions I'm wondering about then this problem may not have been written well.

However I ommitted a given info. If this given info helps you solve this problem, please carry on and respond. So the boat exerts a force of 457 Newtons East on skier 2. And as for the other follow up questions, there is no other information provided. The drag force is simply 325 Newtons. Tell me, does this question make sense at all?

5. Jan 2, 2004

### fffbone

Idealy, the direction of the friction is considered the opposite of the direction in which the subject is traveling. However, the direction and the magnitude of the forces don't seem to match up very well, it might just be me, but the question you posted here is kind of messy, if you organize the question a bit and write it clearly, I might be able to help you more, and maybe draw a diagram.

6. Jan 3, 2004

### craptacular

The question really goes like this

Pardon the messiness and thank you for responding. The question is worded this way:

A motor boat is towing 2 skiers. At a particular moment, the boat exerts a force of 457 Newtons East on the 1st skier and a force of 525 Newtons East 30 degrees South on the 2nd skier. If the boat is moving at a CONSTANT velocity and the drag of friction is 325, find the force that propels the boat. [Key's answer is 1274 Newton East 16 degrees South]

Earlier, someone commented that what the question was really asking was about the reaction force. Can you please comment some more?

I tried looking at all the forces acting on each subject: skier1, skier 2 and the boat. Correct me if I'm wrong but if I draw a free-body diagram on each subject, the forces acting on skier1 alone are the force with which the boat pulls on it [457 Newtons East] and friction which is opposes it AND upon resolving the component of forces along the horizon, the sum of the forces is 0 (since due to motion of constant velocity). Similarly, resolving the components on skier2, the sum of the forces is 0 (due to constant velocity) as well. But what I don't understand is how the drag friction comes into play which is 325 Newtons. Shouldn't this drag friction be the same for all three subjects? Aren't all three subjects moving at a constant velocity, too?

Thanks again.

7. Jan 3, 2004

### Loren Booda

Constant velocity in a medium like water may assume constant viscous force on an object: F(v)=kv=ma. The skiers have friction, a force resolvable into forward and sideways components, biased according to the direction of their skis relative to the boat (ignoring the bias of the propeller).

8. Jan 3, 2004

### Staff: Mentor

Re: The question really goes like this

This seems straightforward. Consider all the forces on the boat. The two skiers exert forces on the boat (use Newton's 3rd law). These forces must be balanced by the force propelling the boat minus the drag. (The drag and the propelling force are along the same line.) All forces add to zero, since it moves at constant velocity.

So... add up the forces due to the skiers. Call the (vector) sum Fskiers. The propelling force minus the drag must be equal and opposite Fskiers.
Don't worry about the skiers. Since they are also moving at constant velocity (we presume) the net force on them must be zero as well. But who cares? (No reason to think that the drag would be the same for all three!)

9. Jan 3, 2004

### craptacular

Thank You Loren B., and fffbone for your comments. I think I know how to tackle this problem now although I still welcome your and anyone else's worked out solution to this problem. Thank you for the good ideas.

Yours truly,
Michael (aka craptacular)