00:01
In this question, we're given that an aeroplane has an airspeed of 580 km per hour bearing 49 north of east.
00:13
Okay, so let's just draw the compass and then draw 49 north of east.
00:21
So this is north, this is east, 49 north of east.
00:28
Is the bearing and that's the plane moving at the speed of 580 kilometers per hour.
00:40
The wind velocity is 40 kilometers per hour in the direction so we have wind moving at this direction we just put this as the direction of the airplane and i'm going to draw another arrow another diagram showing the wind direction 40 kilometers per hour in the direction 32 degrees north of west so this is north this is west sorry and we have 32 degrees north of west that's the wind and it's moving at 40 kilometers per hour next we'll be finding the resultant velocity representing the path of the airplane with respect to the ground and what is the actual ground speed of the aircraft without rounding the final answer.
02:04
So to find the resultant velocity representing the path of the the to find the resultant velocity representing the path of the airline with respect to the ground we're going to proceed as follows.
02:36
The air speed is 580 and the wind velocity is 40.
02:47
So we need to combine these two forces.
02:50
As follows, we're going to have the two arrows, the two vectors, and we're going to use the triangle of the triangle method.
03:01
So the triangle method requires that we connect the head and the tail.
03:07
And so this is the plane speed 580 kilometers per hour.
03:15
And then this is 40 kilometers per hour.
03:20
Then you can bring in the compasses at those two different points.
03:27
If this is 49, this is 51.
03:33
And if this is 51 here, then this should be 49.
03:41
And if this angle here, this angle was given as 32.
03:47
And the resultant is represented by this arrow.
03:55
Okay, so that's the triangle that we need.
03:59
So in this triangle, the combined angle here, 32 plus 49, is 81 degrees, and we want to find the velocity in red.
04:16
So velocity is given in two dimensions...