Velocity of a boat after feeling the wind force

[jahrollins]

Homework Statement

A boat is 400 kg and cruising along with a constant speed of 4.0 m/s in a direction 30 degrees north of east. The boat suddenly begins to feel a force from the wind that is 45 degrees north of east and has a magnitude of 100N. After a 10 second period what is the velocity vector of the boat?

Homework Equations

F = ma
v = v_o + at

The Attempt at a Solution

I'm wondering if I'm doing this right.

So I broke velocity into x and y components

v_xo = 4cos30
v_yo = 4sin30

Found the acceleration : f = ma
100 N = 400 kg * a
a = 1/4 m/s²

Broke acceleration into components
a_x = 0.25cos45
a_y = 0.25sin45

Plugged into equation v_f = v_o + at
v_x = 4cos30 + 0.25cos45 * 10
v_y = 4sin30 + 0.25sin45 * 10

Then I would plug v_x and v_y into Pythagorean to find the magnitude of the velocity? and use inverse tan (v_y/v_x) to find the angle?

 

[xcvxcvvc]

Homework Statement

A boat is 400 kg and cruising along with a constant speed of 4.0 m/s in a direction 30 degrees north of east. The boat suddenly begins to feel a force from the wind that is 45 degrees north of east and has a magnitude of 100N. After a 10 second period what is the velocity vector of the boat?

Homework Equations

F = ma
v = v_o + at

The Attempt at a Solution

I'm wondering if I'm doing this right.

So I broke velocity into x and y components

v_xo = 4cos30
v_yo = 4sin30

Found the acceleration : f = ma
100 N = 400 kg * a
a = 1/4 m/s²

Broke acceleration into components
a_x = 0.25cos45
a_y = 0.25sin45

Plugged into equation v_f = v_o + at
v_x = 4cos30 + 0.25cos45 * 10
v_y = 4sin30 + 0.25sin45 * 10

Then I would plug v_x and v_y into Pythagorean to find the magnitude of the velocity? and use inverse tan (v_y/v_x) to find the angle?

Yes. Everything looks good. Make sure you recognize when you need to correct the arctangent, though! (for example, two negative components)