Sailboat Direction - Kinematics in Two Directions

[bimbambaby]

Homework Statement

A sailboat is traveling east at 5.1m/s . A sudden gust of wind gives the boat an acceleration = (0.80 m/s²}, 40° north of east).

What is the boat's direction 6s later when the gust subsides?

Homework Equations

V_f = V₀ + at

The Attempt at a Solution

To solve I simply created X and Y components of the velocity after those six seconds, in order to use the arctan function to then find my angle:

V_fx = V_ox+at
V_fx = 5.1 m/s + (6s)* (0.80cos40) = 8.777013327 m/s (x)

V_fy = 0 m/s +(6s) * (0.80sin40) = 3.085380526 m/s (y)

To find the angle, I then simply input these values into the arctan function:

tan^-1(vy/vx) = θ
tan^-1(3.085/8.777) = 19°, north of east

This answer, however, is incorrect. Do you have any advice on my approach, or anything that I may be negating my calculations?

 

[joseamck]

Ok here is just a suggestion. Try using 50 as the angle and recalculate the velocities. This I think they were trying to say that the angle of the wind gust it makes with the north is 40 degrees.

 

[bimbambaby]

I appreicate that, but there is a first part of the question that asks for the velocity after 7.7 seconds, in which I used 40° as my angle of reference. I arrived at the correct answer for that. It also says "north of east," which I am sure means north of the negative x-axis (east). I believe that were it phrased otherwise (east of north), that would mean 40° east (to the left) of the positive y-axis, so I don't believe the angles are the issue, unless someone else feels otherwise.

 

[HallsofIvy]

No, "40 degrees N of east" means starting from the east (the x-axis) measure toward the north (counter clockwise) 40 degrees. That is what bimbambaby is doing.

 

[bimbambaby]

Halls of Ivy -

Any idea why the method I employed wouldn't work? I've calculated my velocity components correctly, and that should provide the correct answer, in theory.

 

[azizlwl]

The situation is not like of projectile or free fall.
Once the engine and the wind stops, we assume it to be stopped(maybe it takes a few seconds)

I think the question ask is "where", in direction of x and y.

 

[bimbambaby]

Azizlwl -

I'm not quite sure that I follow your meaning? We're determining the direction of the sailboat in terms of angle relative to the negative (east) x-axis. That is the directional component of the vector.

 

[azizlwl]

We assume the engine is giving the boat a constant velocity due east.
The wind too giving a force that equivalent to acceleration.

We can find the position of the boat after 6s.

After the gust subsides surely the boat is heading east.