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!