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Projectile motion using conservation of energy problem

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data
    A projectile is launched with a speed of 40 m/s at an angle of 60 above the horizontal. Use conservation of energy to find the maximum height reached by the projectile during its flight.



    2. Relevant equations
    KEi + PEi = KEf + PEf (Initial kinetic energy + Initial potential energy of gravity = Final kinetic energy + final potential energy of gravity) rewritten as:
    1/2mvi^2 + mgyi = 1/2 mvf^2 + mgyf
    where:
    vi = initial velocity
    m = mass
    g = acceleration of gravity
    yi = initial y-position
    vf = final velocity
    yf = maximum height/final y-position



    3. The attempt at a solution
    I think I have this solved correctly, and I was wondering if anyone would be willing to confirm the answer I got.

    These are the values I substitute:
    vi = 40 m/s
    g = 9.8 m/s2
    yi = 0 m
    vf = 40 cos(60) (my rational behind this is that at maximum height, the velocity is only in the positive x-direction)
    yf = unknown solving for.

    First, I cancel out the mass in the equation by dividing the entire equation by mass.

    Next, I substitute values, ending up with:
    1/2(40^2) = 1/2 (40 cos60)^2 + (9.8)yf
    800 = 200 + 9.8yf
    600 = 9.8yf
    yf = 61.2 meters
     
  2. jcsd
  3. Mar 4, 2010 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It looks all right.

    ehild
     
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