1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Mechanics - Projectile Motion

  1. Nov 2, 2011 #1
    Problem statement is here: http://www.phys.uri.edu/~gerhard/PHY520/wmex139.pdf

    My approach:
    [tex]y = -\frac{gt^2}{2} + v_0 cos( \alpha) t + h[/tex]

    Projectile hits ground at:
    [tex] t_{gnd} = \frac{v_0 sin( \alpha ) + \sqrt{ v_0^2 sin^2 ( \alpha) + 2gh}}{g}[/tex]

    Now compute derivative of x and solve for alpha:
    [tex]x_{max} = v_0 cos( \alpha) t_{gnd} [/tex]
    [tex]\frac{dx_{max}}{d \alpha} = 0[/tex]

    This last step where you solve for alpha is what buggers me. I get a huge quartic expression in alpha that does not simplify, I suspect the problem setter expects you to make some approximation but I can't figure it out.
  2. jcsd
  3. Nov 3, 2011 #2


    User Avatar
    Homework Helper

    In the first equation (the one for y), it should be sine.

    I see where you're trying to go with your approach. And I think it would work, but maybe you should try a different approach.

    Are you familiar with Lagrange multipliers? Because you've got y=0 as the constraint and x as the function to maximise. The functions x and y are each functions of both alpha and t, so the problem looks well suited to the method of Lagrange multipliers.
  4. Nov 3, 2011 #3
    Worked like a charm, good idea.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook