00:01
In this problem, we're told that we are in a boat that's flowing down a river, and the river is moving at 2 meters per second due south.
00:13
And we're steering the motorboat across the river with a velocity relative to the water of 4 .2 meters per second due east.
00:22
Let's go ahead and draw a sketch of this.
00:24
So here's my river.
00:27
We're told the river is 500 meters wide.
00:29
So there's our 500 meter wide river.
00:35
And the river is flowing down due south at two meters per second.
00:46
And then we're told that we're going to steer the boat due east across the river.
00:52
So here's our velocity vector across the river.
00:54
I'll try to make it about the appropriate size a little bit more than twice as long as that 2 meter per second vector.
01:02
And we're driving due east across the river.
01:07
Okay, the first part of the question asks us, what's the velocity of the boat relative to the earth? so what we're asked to do here, really, is find the resultant of adding those two vectors together.
01:22
So if i add head to tail, that 2 .0 meter per second vector to my 4 .2 meter per second vector, i'll get the resultant, which is the total velocity of the boat, relative to the earth, i'll call that v.
01:42
E.
01:42
Let's go ahead over here and see if i can solve for v .e.
01:46
So the magnitude of v.
01:48
Sub e is just through the pythagorean theorem, going to be the square root of two meters per second squared, plus 4 .2 meters per second squared.
02:02
Just adding the x and the y component.
02:04
Of that resultant vector.
02:07
And so that will come out to be, if you plug it into your calculator, 4 .65 meters per second is the magnitude of the speed...