1. What is the minimum...

what is the minimum energy needed to lift 1.0 kg to a height of 200 km and to give it a speed of 8.0 km/s?
(neglect the small decrease of "g" over that distance)
a) 34 KJ
b) 34 TJ
c) 34 MJ
d) 34 J
e) 34 GJ

2. Originally Posted by Celia
what is the minimum energy needed to lift 1.0 kg to a height of 200 km and to give it a speed of 8.0 km/s?
(neglect the small decrease of "g" over that distance)
a) 34 KJ
b) 34 TJ
c) 34 MJ
d) 34 J
e) 34 GJ
The minimum energy will be the amount of work to lift it 200 km = 2 x 10^5 m plus the amount of kinetic energy we are giving it. (v = 8.0 x 10^3 m/s). ALWAYS convert your units!

So:
$mg \Delta h + (1/2)mv^2$
$= (1.0)(9.8)(2 \, x \, 10^5) + (1/2)(1.0)(8.0 \, x \,10^3)^2$
= 33960000 J = 34 x 10^6 J = 34 MJ.

-Dan