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!

Work and energy: find the total mechanical energy at the max. height of a projectile.

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data
    A 32 kg cannon ball is fired from a cannon with muzzle speed of 1360 m/s at an angle of 44◦ with the horizontal. The acceleration of gravity is 9.8 m/s2 . What is the total mechanical energy at the maximum height of the ball? Answer in units of J.

    2. Relevant equations
    Mechanical energy = KE + UG + US (ignore spring potential energy)
    UG = mgh
    KE = (1/2)mv2

    3. The attempt at a solution
    I actually thought I understood the concepts behind this one fine, but I keep getting the wrong answer.

    First I found the height:
    Theoretically, mechanical energy is conserved, so E at launch = E at top of flight (w/ max height)
    KE + UG = KE + UG
    no UG at launch, and no KE at top of flight in the y-direction -- motion is changing direction -- so
    KE in the vertical direction = UG
    (1/2)(32 kg)(1360sin44 m/s) = (32 kg)(9.8 m/s2)h
    h = 45536.98701 m

    Then, I attempted to find the mechanical energy at the top of the flight.
    Known facts:
    * the mass has a vertical acceleration and a horizontal velocity of 1360cos44 m/s
    * the mass has both kinetic energy (it is moving) and potential gravitational energy.
    * I guessed that the total mechanical energy would be the resultant of these two using the Pythagorean theorem since the two energies are perpendicular to each other.

    E at top = KE in the x-direction + UG in the y-direction
    KE = (1/2)(32)(1360cos44)2 = 15313200.87 J
    UG = (32)(9.8)(45536.98701) = 14280399.13 J

    KE2 + UG2 = resultant2
    resultant = 20938574.93 J

    But... that's the wrong answer.
    Do the directions of the vectors not matter? Can someone provide an explanation for this?
  2. jcsd
  3. Jan 20, 2010 #2


    User Avatar
    Homework Helper

    Re: work and energy: find the total mechanical energy at the max. height of a project

    Energy is scalar, has no direction, you simply have to add the different kinds of energy.

    "KE2 + UG2 = resultant2" this is wrong.

    As for your method, you overcomplicate the calculations. Conservation of the mechanical energy means that the total energy E= KE + PE at the muzzle is the same as at the maximum height.

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