# Velocity of a boat after feeling the wind force

## 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?

F = ma
v = vo + at

## The Attempt at a Solution

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

So I broke velocity into x and y components

vxo = 4cos30
vyo = 4sin30

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

Broke acceleration into components
ax = 0.25cos45
ay = 0.25sin45

Plugged into equation vf = vo + at
vx = 4cos30 + 0.25cos45 * 10
vy = 4sin30 + 0.25sin45 * 10

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

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## 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?

F = ma
v = vo + at

## The Attempt at a Solution

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

So I broke velocity into x and y components

vxo = 4cos30
vyo = 4sin30

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

Broke acceleration into components
ax = 0.25cos45
ay = 0.25sin45

Plugged into equation vf = vo + at
vx = 4cos30 + 0.25cos45 * 10
vy = 4sin30 + 0.25sin45 * 10

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