00:01
Right, so you have an asteroid coming towards earth.
00:03
Initially, it is at a distance of 2 .3 times 10 to the 7 kilometers.
00:12
If we want to put this into meters, that's just going to be 2 .3 times 10 to the 10 meters.
00:22
And we want to find the velocity when it is entering earth's atmosphere.
00:28
So we're also told that that's 100 kilometers.
00:31
So that's our final distance.
00:34
100 kilometers, or 100 times 10 to the 3 meters.
00:40
The mass of the asteroid is 2 .5 times 10 to the 13 kilograms.
00:51
The initial velocity when it's at the initial distance is 8 kilometers per second, or 8 .0 times 10 to the 3 meters per second.
01:08
Okay, so we want to find the final velocity.
01:12
So we just need to find the initial energy and set that equal to the final energy.
01:17
So initially, we're going to have 1 half mv initial squared for the kinetic energy, and then minus g, the gravitational constant, times the mass of earth, times the mass of the asteroid.
01:36
And this here is the mass of the asteroid as well.
01:39
This is divided by d initial.
01:42
So this is our total energy initially, the kinetic and the gravitational potential energy.
01:49
And then when it's right above the surface of the earth, or right above the atmosphere, we have 1 half ma v final squared minus g me ma over d final.
02:10
So we just need to use this equation to solve for v final here.
02:15
First thing we can notice is that the mass of the asteroid is in every term.
02:20
So we can actually just cancel that out, divide everything out, or divide ma out of everything.
02:27
And we'll go ahead and multiply through by 2 to get rid of the 1 half and the 1 half mv squared.
02:33
And that's going to simplify things a bit...