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ecuador · Jan 6, 2007, 08:19 PM

Please help with this physics problem!
a. A 50kg water skier is pulled on a lake by a boat with a horizontal force of 400N. If the wind and current applies another force of 100N at an angle of 30degrees relative to the straight-line direction of the boat, what is the skiers acceleration? B.) what is the acceleration if the wind-current force were in the opposite direction to that in part a).

Capuchin · Jan 7, 2007, 03:55 AM

Hi, this question is concenrning vector addition.

If you draw, on a graph, a line 400 N long in a direction you can call horizontal, then on the end of this draw your 30 degree 100 N force, then the total force felt by the skier is the vector from the start of the 400 N force to the end of the 100 N force.

Hopefully you know how to turn this into a measure of acceleration.

The other part of the question is exactly the same, but with the 100 N force in a different direction.

I hope this helps. Let me know if you need further help.

Capuchin · Jan 7, 2007, 12:10 PM

Well, you can show it using free body diagrams, but the operation you are doing is vector addition, and the easiest way to do that is with a graph...

The other way to do it is to split your forces into vectors along the x and y direction, and add those separately, and then recombine them.
(this uses basic trigonometry)

I'll answer the first part if you want.

I am assuming the wind is blowing against his back at 30 degrees to the boat's vector.
so it is adding 100 cos 30 N to the 400 N of the boat.
There is a further 100 sin 30 N pushing him to one side of the boat.

Using pythagoras we can see the total force is $(100sin(30))^2 + (400 + 100cos(30))^2$

And you can use F = ma to find his velocity and a little trig to find the direction.

If you need further help please feel free to ask :)