00:01
So in this question, we're given some information about an impact with a comet.
00:07
The comet was observed to be nine kilometers across, and the observations showed that the debris or the dust released upon this impact with a speed as low as one meter per second was able to escape the comet.
00:26
So assuming a spherical shape to the comet, we're asked to calculate.
00:30
The mass of the comets and then in part b we need to show something else.
00:37
So we are referred to example 12 .5 and in example 12 .5, a formula is derived for the escape speed of an object and this is equal to the square root of g2gm over r.
01:00
So we can use this formula, we can reverse engineer it to find what the mass of this comet must be since we were given the escape speed.
01:12
So we can square both sides of the equation, so that gives us ve squared, is equal to 2gm over r.
01:23
And then we can multiply both sides of the equation by r and divide by 2g.
01:31
And so that'll give us a formula for the mass equal to ve squared times r divided by 2g.
01:43
And so we can just go ahead and sub in the values that we've been given.
01:48
So one meter per second squared for the escape speed.
01:53
The radius we were given the diameter.
01:56
It's nine kilometers across.
01:58
So the radius is 4 .5 kilometers across or 4 ,500 meters.
02:05
And then we divide by two times the gravitational constant.
02:12
And that will give us a mass for this comet of 3 .37 times 10 to the 13 kilograms.
02:21
So this is the final answer for part a.
02:26
And then in part b, we are asked to calculate how far from the comet's center will the debris be when it has lost 90 % of its initial kinetic energy and how far will it be when it has lost all of its kinetic energy? so this is really a question about conservation of energy.
02:54
So basically in the first part, we want to take 90 % of the initial kinetic energy and set that equal to the change in the potential energy.
03:08
Because as we're losing kinetic energy, that should be converted into potential energy.
03:14
And so that will allow us to calculate an r value for how far away the debris is.
03:22
So what i'm going to do is i'm going to take 90 % or 0 .9 of the initial kinetic energy.
03:30
And i'm going to set that equal to a delta you or a change in potential energy.
03:37
So 0 .9.
03:41
Ek will be equal to the final potential energy minus the initial potential energy...