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 problem) What angle will yield maximum horizontal range?

  1. Feb 28, 2013 #1
    1. The problem statement, all variables and given/known data

    A supply plane is flying at 60.0m/s at an altitude of 200.0m. What angle of flight will yield the maximum horizontal range for the dropped package?

    2. Relevant equations
    1/2(g)(t)2.


    3. The attempt at a solution
    So far the only equations that i have, but may be wrong, is x=((60m/s)cos([itex]\Theta[/itex]))t+1/2(g)(t)2. and y=((60m/s)sin([itex]\Theta[/itex]))t+1/2(g)(t)2+200m. I'm told it would involve a quadratic formula if i do it the more efficient way, but i cannot figure out how to complete it, or if i am going about it all wrong to find the angle that gives the farthest distance. I have also tried messing around with the formulas to try to combine them. I've also thought of using excel to test every angle from 0.0-90.0° but i haven't worked out how i would do that either.
     
    Last edited: Feb 28, 2013
  2. jcsd
  3. Feb 28, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Wily Fury! Welcome to PF! :smile:
    nooo :redface:

    in the x direction, a = … ? :wink:
     
  4. Feb 28, 2013 #3
    the acceleration should be 0 for the x direction?
     
  5. Feb 28, 2013 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

  6. Feb 28, 2013 #5
    i'm still not sure how to approach the next step or if i am on the right track.
     
  7. Feb 28, 2013 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    The next step is to get an expression for the range (as a function of θ).

    Then find the maximum value of the range, either by differentiating wrt θ, or by completing the square. :wink:

    (and now i'm off to bed :zzz:)
     
  8. Feb 28, 2013 #7
    I'm not really sure what that means >.<
     
  9. Mar 2, 2013 #8

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    what what means? :confused:
     
  10. Mar 2, 2013 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You have (correcting your sign for vertical acceleration) x = u cos(θ)t, y = h + u sin(θ)t - gt2/2. Try to answer the following in sequence:
    - at what time (as a function of h, u, g, theta) will the package hit the ground?
    - what will x be at that time?
    - how do you maximise that wrt theta?
     
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 problem) What angle will yield maximum horizontal range?
Loading...