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Find Direction and Angle to arrive directly across initial location?

  1. Feb 13, 2013 #1
    1. The problem statement, all variables and given/known data
    A boat can go 12 km /h in a river that has current of 5 km /h.
    At what angle relative to the shore does the boat have to leave to arrive directly across from initial location?


    2. Relevant equations
    SOH CAH TOA


    3. The attempt at a solution

    I just want some explanation of this question. Would my 12km/h be my hypotenuse and the resultant be the straight line across the river perpendicular to the shore or would my 12km/h be the straight line perpendicular to the shore??

    Because I get 2 different angles if I use tan-1 (5/12) = 22.16 degrees and sin-1 (5/12) which gives me 24.6 degrees.... Which one do I use?
     
  2. jcsd
  3. Feb 13, 2013 #2

    jedishrfu

    Staff: Mentor

    Re: Find Direction and Angle to arrive directly across initial locatio

    No, the 12km/h is the across the river speed and the 5km/h is the river speed so the angle relative to going across the river is tan theta = 5/12. The two speeds add together vectorially giving you a slightly faster speed as you travel across and drift downstream.
     
  4. Feb 13, 2013 #3
    Re: Find Direction and Angle to arrive directly across initial locatio

    I do not understand this, If I want to end up directly across from my initial point, wouldnt the straight line across the river be my resultant and hypotenuse be my 12km/h??
     
  5. Feb 13, 2013 #4

    haruspex

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    Re: Find Direction and Angle to arrive directly across initial locatio

    Yes. Consider e.g. what would happen if the boat's speed relative to the water were less than the speed of the current. Now there's no way to get straight across.
     
  6. Feb 13, 2013 #5
    Re: Find Direction and Angle to arrive directly across initial locatio

    So, I should use sin -1 (5/12)???
     
  7. Feb 13, 2013 #6

    haruspex

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    Re: Find Direction and Angle to arrive directly across initial locatio

    Yes.
     
  8. Feb 14, 2013 #7

    jedishrfu

    Staff: Mentor

    Re: Find Direction and Angle to arrive directly across initial locatio

    Sorry, I misunderstood your question and was looking puely at the math of adding the velocities.
     
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