Boat Hauling Skier: Calculating Acceleration

[bigdaddy]

Homework Statement

A boat is hauling a 250kg skier at an angle of 30 degrees below the horizontal with a force of 200 N. How much is the boat accelerating?

Homework Equations

F=ma

The Attempt at a Solution

I am using the F=ma equation. My only question is how does the 30 degrees play into it? Would it be :

200N= 250kg(cos30) * a? with this I get .03m/s. Which seems somewhat accurate since 200N isn't much force at all. Any ideas?

 

[mgb_phys]

Assuming the 200N force means in the direction of the cable (ie 200N of tension) then then horizontal force on the skier (and so on the boat) is
200N cos(30) = 173N

Then F = ma ,
173 = 250 a
a= 0.69m/s^2

edit - google calculator uses rad for trig functions !

 

[bigdaddy]

Ok. Thanks. That makes sense. At least I had the right equation. Thanks for your help. The 30 degrees threw me off.

 

[mgb_phys]

Instead of remembering cos / sin etc it's better to picture what's happening

If the rope is horizontal (angle=0) then all the force is being used to slow the boat, as the rope drops less force is being applied horizontally, so you need a trig function that starts at 1 for 0 degrees and slowly gets less = cos()