A pilot wants to fly west (ie., the resultant is west). If the plane has an airspeed of 9.5 m/s, and there is a 25m/s wind blowing north, in what direction must she head the plane?
Consider 100seconds flying. The plane goes 950m. So looking at the vector diagram, sinTheta=2500/950 where theta is the angle S of W. This gives a West resultant.
To find the direction in which the pilot must head the plane, we need to consider the effect of the wind on the flight.
Let's break down the velocity vectors involved:
1. Airspeed of the plane: 9.5 m/s towards the west (resultant vector).
2. Wind velocity: 25 m/s towards the north.
Since the wind is coming from the north, it will push the plane off course. To counteract this effect, the pilot needs to adjust the heading of the plane to a certain angle.
To find this angle, we can use vector addition. The resultant velocity (The velocity of the plane with respect to the ground) is the vector sum of the airspeed and the wind velocity.
To visualize this, imagine drawing the vectors on a graph, with the airspeed pointing towards the west (resultant vector) and the wind velocity pointing towards the north.
From the Pythagorean theorem, we know that the magnitude of the resultant vector is equal to
√((9.5)^2 + (25)^2) = √(90.25 + 625) = √715.25 ≈ 26.76 m/s.
To find the direction, we can use trigonometric calculations. The angle θ that the resultant vector makes with due west can be found using the equation:
θ = arctan(25/9.5)
Evaluating this expression, θ ≈ 71.56°.
Therefore, the pilot must head the plane in a direction approximately 71.56° south of west to counteract the wind and maintain a resultant vector towards the west.