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Kinematics problem

  1. Feb 5, 2013 #1
    1. The problem statement, all variables and given/known data

    A hovercraft is traveling 3m/s at 180 deg. The fan of the hovercraft causes a=4m/s2 at 50° for 10 seconds.

    2. Relevant equations

    What is the final velocity?

    3. The attempt at a solution

    v = 3cos180 - 4cos50*10?
     
  2. jcsd
  3. Feb 5, 2013 #2

    gneill

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    Staff: Mentor

    The velocity and acceleration should be vectors with both x and y components. Your attempt doesn't appear to deal with the y-component of the acceleration and its contribution to the final velocity (which will be a vector).
     
  4. Feb 5, 2013 #3
    So do I have to use the same equation with 4sin50° to get the velocity in the y direction, then I can take the magnitude of both vx & vy to get the final velocity?

    Do I have to do the same for the velocity using 3sin180?
     
  5. Feb 5, 2013 #4

    gneill

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    Staff: Mentor

    Sure, sounds good.

    A note on terminology: In general, "velocity" is a vector which has both speed and direction. The magnitude of a velocity vector is the speed. Speed is a scalar quantity with no particular associated direction.
     
  6. Feb 5, 2013 #5
    Ok. I calculated the velocity like so:

    vx = 3cos180 + 4cos50*10 = 22.71 m/s
    vy = 3sin180 + 4sin50*10 = 30.64 m/s

    v = √22.712 + 30.642 = 38.14 m/s --> speed

    I was thinking.....should I use 130° instead of 50°, since the acceleration will be in the same direction as the velocity?
     
  7. Feb 5, 2013 #6

    gneill

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    Staff: Mentor

    That looks fine.
    No, the change in velocity will be in the same direction as the acceleration vector, but the final velocity will have its own angle (with respect to the x-axis). Work out the angle of the velocity vector from your calculated components of the velocity vector.
     
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