1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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. :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: 2d constant motion problem
  1. Hard 2d motion problem (Replies: 1)

  2. Motion in 2D problem (Replies: 7)

Loading...