How Do You Calculate the Wind Force Acting on a Boat?

[triplel777]

Homework Statement

A 331-kg boat is sailing 14.6° north of east at a speed of 1.98 m/s. Thirty seconds later, it is sailing 37.5° north of east at a speed of 4.24 m/s. During this time, three forces act on the boat: a 28.8-N force directed 14.6° north of east (due to an auxiliary engine), a 24.7-N force directed 14.6° south of west (resistance due to the water), and FW (due to the wind). Find the magnitude and direction of the force FW. Express the direction as an angle with respect to due east.

Homework Equations

The Attempt at a Solution

V initial= 1.98cos14.6 + 1.98sin14.6=2.42
V final= 4.24cos37.5 + 4.24sin37.5=5.94
delta V= 3.52
a=v/t so a=3.52/30=0.12m/s2
Ftotal=ma
Ftotal= 331*0.12=39.4
Ftotal= Fw+Fp+Fd
Fp= 28.8cos14.6+28.8sin14.6=35.13
Fd=24.7cos14.6+24.7sin14.6= 30.13
39.4= Fw+35.13+30.13
Fw=-25.86

what am i doing wrong?

 

[kuruman]

V initial= 1.98cos14.6 + 1.98sin14.6=2.42
V final= 4.24cos37.5 + 4.24sin37.5=5.94
what am i doing wrong?

You are not adding vectors correctly. In the above example, you are adding the x and y components of the velocities together. That is absolutely wrong. You have to keep the components separate. The same applies to the addition of the force components. You need to set up two separate sets of equations, one for the x-direction and one for the y-direction. Using unit vector notation helps you do that.

 

[tomcue]

Hello,

Your attempt at solving this problem is a good start, but there are a few errors in your calculations. First, when you calculated the initial and final velocities, you forgot to include the direction in your calculations. For example, the initial velocity should be 2.42 m/s at 14.6° north of east, not just 2.42 m/s. Also, when calculating the acceleration, you need to use the change in velocity (delta V) and the change in time (30 seconds), not just the final velocity. So your acceleration should be 0.117 m/s^2, not 0.12 m/s^2.

Next, when finding the total force, you need to use the correct values for the auxiliary engine and water resistance forces. The auxiliary engine force should be 28.8 N, not 35.13 N, and the water resistance force should be 24.7 N, not 30.13 N. This will give you a total force of 39.4 N, which is correct.

Lastly, to find the magnitude and direction of the wind force, you need to use vector addition. This means adding the x-components and y-components of the forces separately. So the x-component of the total force is 39.4 cos(14.6) = 37.4 N, and the y-component is 39.4 sin(14.6) = 10.4 N. You can then use these values to find the magnitude and direction of the wind force using the Pythagorean theorem and inverse tangent function, respectively. The magnitude of the wind force is 38.7 N, and the direction is 15.2° east of north.

Overall, your approach was correct, but you made some small errors in your calculations. Keep practicing and double-checking your work, and you will improve your problem-solving skills in physics.