00:01
Hi there, so for this world, when we have an airplane that passes directly over a radar station at a time equals to zero.
00:10
So the plane remains an altitude, as is shown here in the figure, four kilometers.
00:17
And it flies with a speed that is given, and that speed is equal to 560 kilometers per hour.
00:27
We're going to let d represent the distance from the range.
00:31
Radar station to the plane and s represents the horizontal distance travel by the plane.
00:40
So with that said, what we need to do is to simply, well, for part a of this problem, we are asked about to express the distance d as a function of s and as a function of the time.
01:02
Okay.
01:03
So from the pythagorean theorem, we know that the distance d is just simply the square root of the distance s squared plus the distance 4 to the square.
01:15
And this to the square.
01:17
Then we can simplify this to just simply the square root of s squared plus 16.
01:24
Now the distance s, that is the distance that the plane travels.
01:32
So that will be the speed that we are given for the plane times the time.
01:35
So that will be the speed that is 560 and this times the time.
01:46
So that's a solution for part a of this problem.
01:51
Now for part b, we are asked about to use the composition to express the distance between the plane and the bird at the station as a function of time.
02:00
So what we need to do is to substitute s, the distance s, into the first equation.
02:07
So that will be that the distance d is just a square root of 560 times the time and up to the square.
02:16
And this plus 16...