# Finding the magnitude and direction

1. Oct 30, 2013

### BOAS

1. The problem statement, all variables and given/known data

A 325Kg boat is sailing 15° north of east at a speed of 2.00ms-1. Thirty seconds later it is sailing 35° north of east at a speed of 4.00ms-1. During this time, three forces act on the boat: A 31N force directed 15° north of east (engine), a 23N force directed 15° south of west (resistance due to water) and Fw (due to the wind). Find the magnitude and direction of the force Fw. Express the direction as an angle with respct to due east.

2. Relevant equations

3. The attempt at a solution

I'm struggling to break this question down into quantities that I know.

From drawing a diagram, the resultant force in the 'forwards' direction is 8N 15° North of east. Which tells me the boat is accelerating due to the engine and the force of the wind, since the direction must also change.

Could anyone point some things out that might help me get started?

Thanks!

2. Oct 30, 2013

### UltrafastPED

Convert everything to rectangular coordinates, then just add 'em up ... then convert back into the nautical form.

The nautical form is fine if you are using a plotting table; we learned to do this when I was a cadet sailor ... geometric vectors!

3. Oct 30, 2013

### BOAS

Right, so I want to break everything I know down into it's x and y components. This is simple enough for the force provided by the engine and the drag of the water. I then know that my force due to the wind needs to change the motion of the boat to 4.00 m/s at 35° north of east. Why is this not given as a force/how do I express this in the same form as the others?

4. Oct 30, 2013

### nasu

The force of the wind you have to calculate .
Write the speeds and the given forces by components.
Calculate the acceleration and then then use newton's second law to calculate the net (total) force necessary to produce this (constant) acceleration.
Knowing the sum of the forces you can find the wind force.

5. Oct 31, 2013

### BOAS

Well, i've made progress but i'm still stuck.

<edit>

I think I have it

Last edited: Oct 31, 2013