00:01
Hi there, so for this problem, we are asked about to determine the word done in propelling a five -thumbed satellite.
00:11
So we will have a five -thumbs satellite to a hide.
00:20
So for part a, to a height of 100 miles.
00:26
So with that said, first of all, we know that because the weight of a body varies inversely as the square of a distance from the center.
00:35
Of the earth, we know that the force is equal to a constant c that we're going to calculate divided by x square, where c is the constant of proportionality.
00:44
Now, because the model of this satellite weighs 5 tons on the surface of the earth, and we know that the radius of the earth, we're going to label that as adds, is approximately a value of 4 ,000, then we can substitute in here and solve for c.
01:03
So that will give us that this is 5.
01:05
Times 4 ,000 to the square.
01:09
So let's see what value we obtained from this.
01:16
So the value that we obtained from this is 80 times 10 to the 6th.
01:22
Now, that's the value that we're going to use for s.
01:26
Now, the work done is just, we go from the 400 ,000 miles to 100 miles about the air.
01:39
So that will be 4 ,100.
01:42
And then the expression that we need to integrate is 80 times 10 to the 6, and this divided by x squared.
01:53
And then we integrate this over x.
01:55
So let's solve this integral...