The piolt of an airplane wishes to fly due north, but there is a 65-km/h wind blowing toward the east. in what direction should the pilot head her plane if its speed relative to the air is 340 km/h?

he wants his westerly component to equal the eastward wind..

65=340SinTheta where Theta is the angle W of N.

To find the direction in which the pilot should head the plane, we need to consider the relative motion of the plane with respect to the wind.

Let's break down the velocities involved:
1. The speed of the plane relative to the air is 340 km/h.
2. The speed of the wind is 65 km/h in the east direction.

Since the wind is blowing to the east, it will affect the plane's course and result in a resultant velocity. For the plane to fly due north, the resultant velocity needs to have a northward component.

To determine the direction in which the pilot should head the plane, we can use vector addition. The resultant velocity (Vr) of the plane can be calculated as the vector sum of the velocity of the plane (Vp) and the velocity of the wind (Vw).

Vr = Vp + Vw

The magnitude of the resultant velocity can be calculated using the Pythagorean theorem:

|Vr|^2 = |Vp|^2 + |Vw|^2

Let's substitute the given values into the equations:

|Vr|^2 = (340 km/h)^2 + (65 km/h)^2

|Vr|^2 = 115600 + 4225

|Vr|^2 = 119825

Taking the square root of both sides gives:

|Vr| = sqrt(119825) ≈ 346.36 km/h

Now, to find the direction of the resultant velocity, we can determine the angle it makes with the north direction.

Let's use trigonometry to find the angle θ:

θ = arctan(|Vw| / |Vp|)

θ = arctan(65 km/h / 340 km/h)

θ ≈ 10.84°

Therefore, the pilot should head the plane in a direction approximately 10.84° east of north to counteract the effect of the wind and achieve a due north course.

To determine the direction the pilot should head the plane, we need to find the resultant velocity, which is the vector sum of the plane's velocity relative to the air and the wind's velocity. We can use vector addition to find the direction.

Given:
Wind speed = 65 km/h towards the east
Plane speed relative to the air = 340 km/h

Since the wind is blowing towards the east, we can represent the wind's velocity as a vector (65 km/h, 0°).

The plane's relative velocity is its speed relative to the air (340 km/h) and its direction is due north, which we can represent as a vector (340 km/h, 90°).

To find the resultant velocity, we add the vectors of the wind and the plane's velocity:

(340 km/h, 90°) + (65 km/h, 0°)

To simplify vector addition, we convert the wind's velocity into components:

Wind's velocity towards the east = 65 km/h
Wind's velocity towards the north = 0 km/h

Now we can add the components:

(340 km/h + 0 km/h, 90° + 0°)

Simplifying, we get:

(340 km/h, 90°)

Therefore, the pilot should head her plane in a direction of 90°, which is due east.