CATAGORY: Mechanics
QUESTION: A plane, travelling at 800 m/s and 1000 m above the earth, drops
a bomb weighing 500 kg.   How long (in seconds) will it take the bomb to
strke the earth and how far (in meters) will the bomb travel before
striking the earth?

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The horizontal and vertical motions are independant they are described
by

(1)      Y = Yo +  Vo,y t -.5 g t^2
         X = Xo +  Vo,x t
         
Where Xo is the initial horizontal position which we take to be equal
to zero, Yo is the initial vertical position which we take to be
1000m, Vo,y is the initial vertical velocity = 0m/s, Vo,x is the
inital horizontal velocity = 800m/s and g =9.8m/s^2.  This gives us

(2)     Y = 1000m -4.9m/s^2 t^2
        X = 800m/s t
        
When Y = 0 the bomb hits the ground so we have

(3)    0 = 1000m - 4.9m/s^2 t^2

Solving for t

(4)      t = sqrt(1000m/4.9m/s^2) = 14.29 s

In that time the bomb travels horizontaly

(5)     X = 800m/s x 14.29s = 11432 m ~11400       

          ********************************
          *                              *
          *   X ~ 11400m meters ahead of *
          *   where it was dropped.      *
          *                              *
          ********************************