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Kinematics calculation

  1. Sep 15, 2009 #1
    1. The problem statement, all variables and given/known data
    A ship cruises forward at Vs= 5 m/s relative to the water. On deck, a man walks diagonally toward the bow such that his path forms an angle of 25 degrees with a line perpendicular to the boat's direction of motion. He walks at Vm= 3 m/s relative to the boat. What is his velocity relative to the water? And at what angle to his intended path does the man walk with respect to the water?


    2. Relevant equations
    vector magnitude and dot product


    3. The attempt at a solution
    I found the velocity of the man to be 7.8224 m/s by finding the x component of the velocity vector and the y component and then taking the magnitude. Our instructor told us we should use the dot product to find the angle that the man walks relative to the water, and I'm not sure if I calculated it right. I came up with 64.998 degrees.
     
  2. jcsd
  3. Sep 15, 2009 #2

    rl.bhat

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    Velocity vector is written as
    v = (vx*i + vy*j) vb = vb*i
    So cosθ = v.vx/(v*vb)
     
  4. Sep 15, 2009 #3
    So, our instructor helped us with the velocity magnitude. He gave [(5 + 3*cos25)^2 + (3*sin25)^2]^(1/2), is this not correct?
     
  5. Sep 15, 2009 #4

    rl.bhat

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    That is correct.
    The formula in my post is to find the angle between the resultant velocity and the velocity of the boat with respect to the water.
     
  6. Sep 15, 2009 #5
    So, is it supposed to be cos(theta) = v*vx/(v*vb)? And is vb the velocity of the boat?
     
  7. Sep 15, 2009 #6

    rl.bhat

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    Yes.
     
  8. Sep 15, 2009 #7
    Thank you very much for your help!!
     
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