An airplane's velocity with respect to the air is 580 mph and it is headed towards N 58° W. The wind, at the altitude of the plane, is from the southwest and has a velocity of 60 mph. What are the resultant speed and direction of the airplane?
To find the resultant speed and direction of the airplane, we need to consider the effect of the wind on the airplane's motion.
Let's break down the given information:
The airplane's velocity with respect to the air: 580 mph, heading towards N 58° W
Wind velocity: 60 mph from the southwest
To find the resultant speed, we can use vector addition. We add the velocities of the airplane and the wind to get the relative velocity of the airplane:
Relative velocity = Airplane velocity + Wind velocity
To find the direction of the resultant velocity, we can use trigonometry. Since the airplane is heading towards N 58° W, we need to find the angle between the resultant velocity and the north direction.
Let's calculate the resultant speed first:
Airplane velocity = 580 mph
Wind velocity = 60 mph
Relative velocity = Airplane velocity + Wind velocity
Relative velocity = 580 mph + 60 mph
Relative velocity = 640 mph
Now let's calculate the direction of the resultant velocity:
The angle between the resultant velocity and the north direction can be found using trigonometry.
In this case, the airplane is heading N 58° W, which means the angle between the resultant velocity and the north direction will be 90° - 58° = 32°.
Therefore, the resultant speed is 640 mph and the resultant direction is N 32° W.