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: Conservation of energy problem (projectile with air drag)

  1. Nov 1, 2008 #1
    1. The problem statement, all variables and given/known data

    A stone with weight w is thrown vertically upward into the air from ground level with initial speed v0. If a constant force f due to air drag acts on the stone throughout its flight, (a) show that the maximum height reached by the stone is

    [tex] h = \frac{v_0^2}{2g(1+f/w)} [/tex]

    (b) Show that the stone's speed is

    [tex] v = v_0 \left( \frac{w-f}{w+f} \right) ^ {1/2} [/tex]

    just before impact with the ground.

    2. Relevant equations

    work done by an external force = change in energy

    3. The attempt at a solution

    I have no trouble with part (a). I need help with (b)

    W_{air} &= (-f) * (2h) \\
    &= -2fh \\
    &= -2f\frac{v_0^2}{2g(1+f/w)} \\
    & = -2f\frac{v_0^2 w}{2g(w+f)}

    [tex]W_{air} = \Delta E = \Delta K = \frac{1}{2}m(v^2 - v_0^2) = \frac{w}{2g}(v^2 - v_0^2)[/tex]

    We can set the two expressions equal

    -2f\frac{v_0^2 w}{2g(w+f)} &= \frac{w}{2g}(v^2 - v_0^2) \\
    -2f\frac{v_0^2 }{(w+f)} &= v^2 - v_0^2 \\
    v^2 &= v_0^2 + -2f\frac{v_0^2 }{w+f} \\
    &= v_0^2 \left( \frac{1-2f}{w+f} \right)

    But this is wrong. Can anyone tell me where I messed up?
  2. jcsd
  3. Nov 1, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi azure kitsune! :smile:

    Only the last line is wrong. :cry:
  4. Nov 2, 2008 #3
    Waaahhhh!!! *feels so stupid!!!*

    Thanks tiny-tim. :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook