00:01
All right, so we have this rocket that is taking off from the south pole.
00:05
It reaches the height of 250 kilometers when its engines burn out, and it is going a speed of 6 kilometers per second at that point.
00:16
And we want to know just how high it goes before earth's gravity takes over and it crashes back down to earth.
00:22
So for this, we can use conservation of energy.
00:25
The kinetic energy at 250 kilometers plus the potential energy there has to equal the kinetic energy plus potential energy at any point along its journey.
00:35
So we can set this kinetic energy to be zero to find the height at which it will crash.
00:41
So we have an equation for the kinetic energy, one half mv squared.
00:45
And then negative potential energy at the 250 kilometer mark, where this r is going to be the radius of the earth plus that 250 kilometers.
00:56
And then over here we have zero for the kinetic energy plus the potential energy at some new distance r2.
01:04
If we divide all terms by the little mass, the mass of the rocket, we can then solve for r2 by multiplying through by r2.
01:16
And we get one half, or we get g times m on the top negative g times m right here.
01:24
And then we're going to multiply through by r2...