A pilot wants to fly a plane directly eastward when the wind is from the north at 55 miles per hour. if the air speed is 230 miles per hour, in what direction must the plane be headed?

Draw the vector diagram. The southerly component of the air speed must equal 55mph South

So in my mind, I see 230SinTheta=55

What kind of physics class uses mph? Goodness.

8.18 m/s

To determine the direction the plane must be headed, we need to consider the effect of the wind on the plane's motion.

Let's break down the velocity vectors involved:

1. The airspeed of the plane is 230 miles per hour, which means the plane can move at this speed relative to the air mass.

2. The wind is coming from the north at a speed of 55 miles per hour. This means the wind is blowing in a direction towards the south.

Now, to find the actual ground speed and direction of the plane, we need to add the vectors of the plane's airspeed and the wind's velocity.

Since the wind is blowing from the north, and we want the plane to fly directly eastward, the pilot needs to compensate for the wind's effect. To do this, the pilot must point the plane slightly into the wind. This means the plane's direction will be slightly northeast of east.

To find the exact direction, we can use trigonometry. We have a right triangle with the north component of the wind velocity (55 mph) and the east component of the plane's airspeed (230 mph) as the legs.

Using the Pythagorean theorem, we can solve for the resultant of these two vectors:

Resultant speed = sqrt((North component)^2 + (East component)^2)
= sqrt((55 mph)^2 + (230 mph)^2)
= sqrt(3025 + 52900) mph
= sqrt(55925) mph
≈ 236.5 mph

To find the direction, we can use the tangent of the angle.

Tangent(angle) = (North component)/(East component)
= 55 mph / 230 mph
≈ 0.2391

Now, find the arctangent of 0.2391 to get the angle:

angle ≈ arctan(0.2391)
≈ 13.49 degrees

Therefore, the plane must be headed approximately east-northeast (ENE) at an angle of 13.49 degrees.

To determine the direction in which the plane must be headed, we need to consider both the wind speed and the airspeed.

Let's break it down step by step:
1. Draw a diagram: Draw a compass rose, indicating north, south, east, and west. Label one axis as "North-South" and the other axis as "East-West".

2. Wind vector: Since the wind is coming from the north, we need to draw a vector pointing southward with a magnitude of 55 miles per hour (mph). Label it as "Wind".

3. Airspeed vector: The airspeed refers to the speed of the plane relative to the air. In this case, the airspeed is 230 mph, and since we want to fly directly eastward, draw a vector pointing east with a magnitude of 230 mph. Label it as "Airspeed".

4. Resultant vector: To determine the direction the plane must be headed, we need to find the resultant vector, which represents the combined effect of the wind and airspeed. To do this, we add the wind vector and the airspeed vector. Connect the tail of the airspeed vector to the tip of the wind vector.

5. Measure the resultant vector: Use a protractor or ruler to measure the angle between the resultant vector and the eastward direction. This angle represents the direction the plane must be headed.

Once you have measured the angle, you can determine the direction by comparing it to the compass rose on the diagram. If the angle is greater than 90 degrees, the plane must be headed north of east. If the angle is less than 90 degrees, the plane must be headed south of east.

By following these steps, you can determine in which direction the plane must be headed considering the wind and airspeed.