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2-D Motion and Vectors

  1. Sep 23, 2013 #1
    1. The problem statement, all variables and given/known data

    A Coast Guard cutter detects an unidentified ship at a distance of 20.0 km in the direction 15.0° east of north. The ship is traveling at 26.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat to intercept and investigate the vessel. (a) If the speedboat travels at 50.0 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north. (b) Find the time required for the cutter to intercept the ship.


    2. Relevant equations
    Ax=Acosθ
    Ay=Asinθ
    x=Vit+(1/2)at2

    3. The attempt at a solution
    Honestly, I don't know how to go about drawing this problem up. If some one could help me set this up, I would be able to answer it.
     
  2. jcsd
  3. Sep 23, 2013 #2

    rude man

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    At t = 0 assume the cutter is at x = y = 0, so the ship is at what position?

    So what is the ship's position for all t > 0? And, assuming an angle θ for the cutter (with North), what is the cutter's position for all t > 0?

    Part (b) can wait until you've solved part (a).
     
  4. Sep 23, 2013 #3

    Simon Bridge

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    Start by sketching out the situation.
    Draw the position of the coastguard boat, then the position of the unidentified ship.
    Draw a velocity vector for the ship - Draw an indication of where, roughly, the velocity of the speedboat points.

    Notice that while the speedboat travels, the unidentified ship also changes position.

    You can do this as a relative motion problem or as a speed-displacement problem.
     
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