If a projectile is launched vertically from the surface of the earth with a speed equal to the escape speed, how high above the Earth's surface is it when its peed is half the escape speed.

Why can't I use the V=(GM(mass of the earth)/(R(earth+H))^(1/2)

Question

If a projectile is launched  vertically from the surface of the earth with a speed equal to the escape speed, how high above the Earth's surface is it when its peed is half the escape speed.

Why can't I use the V=(GM(mass of the earth)/(R(earth+H))^(1/2)

anonymous · Answer

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apply conservation of energy::
total mechanical energy at surface=total mechanical energy at final
1/2m(Ve)^2=1/2m(Ve/2)^2+mgh.....find h from here....