(v = [velocity], vbar = [average velocity], t = [time], d = [distance], e = [energy], 241350 = 150 [miles] in [meters], 10 = [acceleration] due to gravity, gbar = average force exerted by gravity during the drop, 5.98E24 = Mass of earch in KGs)

   v = at
vbar = at/2
   t = d/vbar

vbar = at/2
vbar = 5t

   t = d/5t
5t^2 = 241350
 t^2 = 48270
   t = 219.7

   v = at
   v = 10*219.7
   v = 2197 m/s

The [elephant] impacts at just under 3.5 times the speed of sound. I am sure it may [smart a bit], but not enough to destroy all living things on the [earth].

Now, if e = 1/2 mv^2 and we use [The Custodian]'s figure of 4.184E12 Joules per kiloton. If you want to aim for 10,000 atomic bombs worth of energy, then we need to drop the elephant from a little higher up.

I am assuming for the purposes of argument that an atomic bomb is 1 Megaton (forget about the bomb that totalled [Hiroshima], technology has moved on since then).

First, lets calculate the total energy required:

e = (total number of bombs) * (power of each bomb in kilotons) * (joules per kiloton)
e = 10,000 x 1,000 x 4.184E12
e = 4.184E19

We can now work out how fast this elephant needs to be going:

e = 1/2mv^2
4.184E19 = 1/2 x 7000 x v^2
v^2 = 4.184E19 / 3500
v = 1.093E8 m/s

Now we are getting to the point, all we need to do is [accellerate our elephant] to just over 1/3 of the [speed of light].

The next part is trickier, we need to find the altitude required to drop the [elephant]. Assuming a steady accelleration of 10m/s/s, this would be easy, but gravity is [inversly proportional] to the square of distance, and I have a feeling that this will come into play with these figures.

                           f = ma
                           v = at => t = v/a
                           t = d/vbar

                        vbar = 1.093E8 ^ 0.5
                             = 1.045E4

                         v/a = d/1.045E4
                   1.093E8/a = d/1.045E4
                   a/1.093E8 = 1.045E4/d
                           a = 1.142E12/d

                           a = 6.672E-11 * 5.98E24 / ((6.38E6+d)*(6.38E6+d)) (stolen from gsu.edu)
                           a = 3.99E14 / (4.07E12 + 1.276E7d + d^2)
                           a = 9.80 + 3.12E7/d + 3.99E14/(d^2)

                  1.142E12/d = 9.80 + 3.12E7/d + 3.99E14/(d^2)
                    1.142E12 = 9.80d + 3.12E7 + 3.99E14/d
           9.80d + 3.99E14/d = 1.142E12
9.80d - 1.142E12 + 3.99E14/d = 0

Solve as a [quadratic equation] and d = 116524244548.55304

This works out at just over 116 million kilometers. Note, for this to work properly, you will have to remove all matter in the [Solar System] which is not part of the [Earth], but this is left as an exercise for the reader.

How to destroy the world using a spaceship and an elephant