(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.