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Homework Help: Velocity of a boat after feeling the wind force

  1. Feb 5, 2010 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations
    F = ma
    v = vo + at

    3. 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?
  2. jcsd
  3. Feb 5, 2010 #2
    Yes. Everything looks good. Make sure you recognize when you need to correct the arctangent, though! (for example, two negative components)
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