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Homework Help: 2d constant motion problem

  1. Aug 17, 2014 #1
    So I have a boat going across a river (y-direction, north) 400m wide.
    I am trying to hit a target 75m in the positive x direction on the opposite side of the river.
    My boat will travel a velocity v.
    The river will provide a constant velocity of +0.5 (east)

    I am trying to find the angle a, north of west to point my boat.

    hope that all makes sense.

    so far I have:

    y = vt or t = y/v
    t = 400 / v*sin(a)

    x = vt
    75 = [0.5 - cos(a)] * t

    then I plugged in t

    75 = 200/[v*sin(a)] - [400*v*cos(a)]/[v*sin(a)]

    I cant seem to solve this. Am I doing this the right way?

    I was thinking I need another function and I remember having to use
    sin(a)^2 + cos(b)^2 = 1
    for something like this a while back. And if I do, how do I? Do I just solve the first two equations for sin and cos and then plug the equations in to the third, expand them, then solve another for t and then plug it in and simplify?

    any help would be greatly appreciated.
  2. jcsd
  3. Aug 17, 2014 #2


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    2017 Award

    Hello Kurt, sorry you missed the template. Please use it.

    I wonder if your river velocity is 0.5 nautical miles per fortnight or 0.5 m/s, because you missed giving the units. With an error as a consequence:

    If you had written your second relevant formula (under 2. in the template) as

    75 m = [0.5 m/s - cos(a)] * t

    you would have immediately seen that it is nonsense to add a cosine to a velocity (how long is a year plus one ?)

    However, this appears to be a typo omission, because under "3. attempt at solution", the v pops up again.

    A second error pops up if you temporarily assume the river not to flow. a can then be zero, but instead of t = 400 m / v you get a divergence. You want to interchange cos and sin.

    For the rest, you're okay:
    vt cos(a) = 400 m plugged in to the second eqn gives you
    $${75\over 400}v\cos\alpha = 0.5 - v \sin\alpha$$
    which is a simple goniometric equation of the form ##a \cos\alpha + b\sin\alpha = c##.
    The relevant expression to help you solve that is ##\sin(\alpha+\beta) = ...##
  4. Aug 17, 2014 #3
    thanks. sorry for missing the units and for the typo also. I'll give it another crack. :)
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