Sailboat in the wind problem. (Kinematics) Conceptual question.

[Sentience]

Homework Statement

A sailboat is traveling east at 5.0 m/s. A sudden gust of wind gives the boat an acceleration a =(0.80 m/s^2 and 40 degrees north of east).

Homework Equations

V = Vo + at
X - Xo = Vo*t + .5at^2
V^2 = Vo^2 + 2a(X - Xo)

The Attempt at a Solution

I ended up getting the correct answer of 9.21 m/s, 19.6 degrees north of east.

However, the first several times when I tried to calculate the direction part of the vector, I found the angle by solving for the final positions of x and y and solving for the angle in that triangle. (Instead of using the x and y velocity components to solve for the angle).

I guess conceptually I don't understand why I have to use the velocity x and y components instead of the final positions of x and y to find direction.

 

[tedbradly]

Homework Statement

A sailboat is traveling east at 5.0 m/s. A sudden gust of wind gives the boat an acceleration a =(0.80 m/s^2 and 40 degrees north of east).

Homework Equations

V = Vo + at
X - Xo = Vo*t + .5at^2
V^2 = Vo^2 + 2a(X - Xo)

The Attempt at a Solution

I ended up getting the correct answer of 9.21 m/s, 19.6 degrees north of east.

However, the first several times when I tried to calculate the direction part of the vector, I found the angle by solving for the final positions of x and y and solving for the angle in that triangle. (Instead of using the x and y velocity components to solve for the angle).

I guess conceptually I don't understand why I have to use the velocity x and y components instead of the final positions of x and y to find direction.

Homework Statement

Homework Equations

The Attempt at a Solution

Because you're looking for the direction of the velocity, not the displacement. In this case, both the displacement vector and velocity vector will have the same direction (if you take the starting point to be x = 0 and y = 0 for displacement).

You were one arbitrary decision away from getting the wrong answer by using displacement. What if I said the origin was x = 0 y = 100 trillion? Then, the final position would be x = something small and y = ~100 trillion. The angle would be ~90 degrees.

If you instead find the angle of the velocity vector directly, you always get the right answer.

 

[willem2]

).

You were one arbitrary decision away from getting the wrong answer by using displacement. What if I said the origin was x = 0 y = 100 trillion? Then, the final position would be x = something small and y = ~100 trillion. The angle would be ~90 degrees.

If you instead find the angle of the velocity vector directly, you always get the right answer.

Actually, I think the boat starts going east and then gets accelerated over time to a velocity north of east, so it will go in a curve, and the direction will be in a different direction as the displacement.
I think the problem statement lacks the amount of time that the acceleration lasts.

 

[tedbradly]

Actually, I think the boat starts going east and then gets accelerated over time to a velocity north of east, so it will go in a curve, and the direction will be in a different direction as the displacement.
I think the problem statement lacks the amount of time that the acceleration lasts.

I see. Yes, thank you.

 

[rwisz]

As a scientist, it is important to understand the concept behind the equations and how they relate to the problem at hand. In this case, we can use the equations of kinematics to solve for the final velocity and position of the sailboat after the gust of wind. However, the direction of the sailboat's velocity is not determined by its final position, but rather by its velocity components in the x and y directions. This is because the sailboat's direction is determined by the direction in which it is moving, not its final position. Therefore, to accurately determine the direction of the sailboat's velocity, we must use the velocity components in the x and y directions. This allows us to understand the direction in which the sailboat is traveling and how it is affected by the gust of wind. By using the correct approach, we can ensure that our calculations are accurate and our understanding of the problem is clear.