Solving Sailboat Problem: Magnitude and Direction of Wind Velocities

[ridlejs]

Homework Statement

The force exerted by the wind on a sailboat is approximately perpendicular to the sail and proportional to the component of the wind velocity perpendicular to the sail. For the 950 kg sailboat shown in Figure P4.54, the proportionality constant is given below.


Water exerts a force along the keel (bottom) of the boat that prevents it from moving sideways, as shown in the figure. Once the boat starts moving forward, water also exerts a drag force backwards on the boat, opposing the forward motion. If a 18 knot wind (1 knot = 0.514 m/s) is blowing to the east, and the sailboat is heading directly north at a speed of 16 knots, determine the magnitude and directions of the wind velocity as measured on the boat.

The boats sail is at a 30 degree angle pointing SE.
Determine magnitude and direction of wind velocities.

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What is the component of the wind velocity in the direction parallel to the motion of the boat?

Homework Equations

sqrt x^2+y^2

The Attempt at a Solution

I do not know really where to begin, I thought to find x and y component, I should just plug in 18*.514cos30 and sin 30, then square the two, add, and take square root. Also, I do not understand why a perpendicular force does not have a 0 x component? Any help greatly appreciated.

 

[tiny-tim]

Welcome to PF!

… I do not understand why a perpendicular force does not have a 0 x component?

Hi ridlejs ! Welcome to PF!

You're right that the component of a force perpendicular to the force is 0.

But here, the wind is the force, and you are asked for the component of the force perpendicular, not to the wind, but to the sail.

So it's cosine of the angle between the wind and the perpendicular to the sail (or sine of the angle between the wind and the sail).

I do not know really where to begin, I thought to find x and y component, I should just plug in 18*.514cos30 and sin 30, then square the two, add, and take square root.

Sorry, not following you.

Please give more detail!

 

[Moetasim]

I would first clarify any uncertainties or questions about the problem statement. In this case, I would ask for clarification on the given information, such as the direction and orientation of the sailboat, the angle of the sail, and the location of the wind velocity measurement on the boat. This will ensure that the solution is accurate and based on all the relevant information.

Next, I would approach the problem by breaking down the given information into components and using vector addition to determine the overall magnitude and direction of the wind velocity. The perpendicular force of the wind on the sail can be broken down into x and y components, with the x component being parallel to the direction of the boat's motion and the y component being perpendicular to it. The magnitude of the wind velocity can then be determined using the Pythagorean theorem.

To address the question about the perpendicular force not having a 0 x component, this is because the boat is not perfectly aligned with the wind direction. The angle of the sail creates a component of the wind velocity that is perpendicular to the boat's motion, resulting in a force that is not entirely parallel to the boat's direction. This can be visualized using vector diagrams.

Overall, the solution to this problem would involve using vector calculations and trigonometry to determine the magnitude and direction of the wind velocity on the boat. It is important to carefully analyze and understand the given information and clarify any uncertainties before attempting to solve the problem.