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: Cannon Ball r(t)

  1. Sep 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Question: A cannon shoots a ball at angle Ø above the horizontal ground. Neglecting air resistance, and letting r(t) denote the ball's distance from the cannon, What is the largest possible value of Ø if r(t) is to increase throughout the ball's flight? [hint: Write down r2 as x2 + y2, and then find the condition that r2 is always increasing.]

    2. Relevant equations

    r(t) = gt2/2 + v0t + x0
    r2 = x2 + y2
    x = rcosØ
    y = rsinØ

    3. The attempt at a solution

    r2 = (gt2/2 + v0t + x0)(gt2/2 + v0t + x0) = x20 + 2x0v0t + x0gt2 + v20t2 + v0gt3 + g2t4/4 = x2 + y2 = r2(cos2Ø + sin2Ø)

    I don't know how to solve for Ø, so that r2 is always increasing.
  2. jcsd
  3. Sep 14, 2010 #2
    1) There shouldn't be any gravity in the x-direction.
    2) You have to find dr^2/dt > 0 if r^2 is going to always increase
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook