Sailboat Acceleration Calculation

In summary, the force exerted by the wind on a sailboat is proportional to the component of the wind velocity perpendicular to the sail, and the force exerted by water along the keel prevents sideways movement while also creating a drag force opposing forward motion. To find the initial acceleration of a 950-kg sailboat with a 15-knot eastward wind, the force exerted by the wind perpendicular to the sail must be calculated and used in the equation F = ma. By separating the force into its x and y components, the acceleration can be determined.
  • #1
DriverX
2
0
Initial Acceleration?

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 the figure below, the proportionality constant is
da.gif


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 15-knot wind (1 knot = 0.514 m/s) is blowing to the east, what is the initial acceleration (m/s2) of the sailboat?

diagram.gif
 
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  • #2
Welcome to PF!

Hi DriverX! Welcome to PF! :smile:

But … is that picture really a sailboat? :confused:

It looks more like a horse! :biggrin:
 
  • #3


p4-54.gif
 
  • #4
that's better! :biggrin:

ok …
DriverX said:
The force exerted by the wind … is … proportional to the component of the wind velocity perpendicular to the sail.

… so find the force exerted by the wind perpendicular to the sail, and so find the forward force, and use F = ma.

What do you get? :smile:
 
  • #5


Driver
because a force is a vector and the question is in two dimensions, i.e X and Y,
you can separate the force into it's x and y components

e.g if you push a block north east (like your sail) at an angle of 45 degrees
your F vector, is really two forces, one going east in the X direction, and one going north in the Y direction,

so the Feast = Fcos45 degrees
and Fnorth = Fsin45 degrees

you can use this concept (i think? ) to help solve your question
 

1. What is initial acceleration?

Initial acceleration is the rate of change of an object's velocity at the very beginning of its motion. It describes how quickly an object's speed is increasing or decreasing at the start of its movement.

2. How is initial acceleration calculated?

Initial acceleration can be calculated by dividing the change in an object's velocity by the time it takes for that change to occur. The formula for initial acceleration is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What factors affect initial acceleration?

Initial acceleration is affected by the mass and force of an object. Objects with larger masses require more force to accelerate at the same rate as objects with smaller masses. Additionally, the direction and magnitude of the applied force also impact initial acceleration.

4. How does initial acceleration relate to Newton's laws of motion?

Initial acceleration is related to Newton's First Law of Motion, which states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an unbalanced force. Initial acceleration is the result of an unbalanced force acting on an object, causing it to change its velocity and accelerate.

5. How is initial acceleration different from average acceleration?

Initial acceleration represents the acceleration of an object at the very beginning of its motion, while average acceleration represents the overall acceleration of an object over a period of time. Average acceleration takes into account any changes in velocity that occur throughout the entire motion, while initial acceleration only considers the change in velocity at the start of the motion.

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