A plane is flying with an airspeed of 200 miles per hour and heading 150°. The wind currents are running at 30 miles per hour at 175° clockwise from due north. Use vectors to find the true course and ground speed of the plane. (Round your answers to the nearest ten for the speed and to the nearest whole number for the angle.)

Question

A plane is flying with an airspeed of 200 miles per hour and heading 150°. The wind currents are running at 30 miles per hour at 175° clockwise from due north. Use vectors to find the true course and ground speed of the plane. (Round your answers to the nearest ten for the speed and to the nearest whole number for the angle.)

Answer 1

draw the diagram. Add the wind vector to the speed vector (head to tail). The resultant from the origin to the head of wind is now the resultant. Label it R.

You have two sides, and the angle between S and W. Figure it out. I see it as in my head as the 360-30-175 =155 check that.

R^2=200^2 + 30^2 - 2*200*30Cos155

grab your calculator, and find R

Answer 2

A plane fre

Answer 3

To solve this problem, we can use vector addition.

Let's first break down the velocities into components.

The airspeed of 200 miles per hour at 150° can be broken down into horizontal and vertical components. The horizontal component (x-axis) can be found by multiplying the magnitude of the airspeed by the cosine of the angle. The vertical component (y-axis) can be found by multiplying the magnitude of the airspeed by the sine of the angle.

Horizontal component of airspeed = 200 * cos(150°)
Vertical component of airspeed = 200 * sin(150°)

Similarly, we can break down the wind currents of 30 miles per hour at 175° into horizontal and vertical components using the same process.

Horizontal component of wind = 30 * cos(175°)
Vertical component of wind = 30 * sin(175°)

Now, let's add the horizontal components and vertical components separately to find the overall horizontal and vertical velocities.

Horizontal velocity = Horizontal component of airspeed + Horizontal component of wind
Vertical velocity = Vertical component of airspeed + Vertical component of wind

Next, we can use the Pythagorean theorem to find the magnitude of the resulting velocity:

Magnitude of velocity = square root of (Horizontal velocity^2 + Vertical velocity^2)

Finally, to find the course angle, we use the inverse tangent function:

Course angle = arctan(Vertical velocity / Horizontal velocity)

By following these steps, we can calculate the true course and ground speed of the plane.