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Final Kinetic Energy and speed of three projectiles fired from a building's roof

  1. Nov 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Three different mass projectiles, mA > mB > mC, are launched from the top of a building at different angles with respect to the horizontal. Each particle has the same initial kinetic energy.

    Which particle has the greatest kinetic energy just as it hits the ground? Why?
    Which particle has the greatest speed just as it hits the ground? Why?

    2. Relevant equations

    (KE + PE)i = (KE + PE)f
    KE = .5 mv^2
    PE = mgh

    3. The attempt at a solution

    I don't know if it is the particle that has the highest mass m or attains the highest height h. Obviously, the one that attains the highest point will have the highest final velocity. vf = sqrt(2gh)

    My teacher said that's wrong and now I don't know what to put.
     
  2. jcsd
  3. Nov 3, 2011 #2
    Hint: What can you say about the kinetic energy of each projectile as it reaches the same level as when it was launched? At that point, think about potential energy.
     
  4. Nov 3, 2011 #3
    Hmm that is very helpful. At the point where they were launched, the energy of each projectile would equal its initial kinetic energy. So the initial kinetic energy + mgh at that point would equal the total energy, so mA has the highest?
     
  5. Nov 4, 2011 #4
    Yes, you are correct.

    Each projectile will have its speed increased by (2gh)^.5 when it hits the ground. That implies something about which one is going the fastest when it hits.

    This is all the assistance I can give. I'll be away from a computer for the next few days.
     
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