An airplane pilot wishes to fly due west. A wind of 90.0 km/h is blowing toward the south.If the airspeed of the plane (its speed in still air) is 305.0 km/h , in which direction should the pilot head?
To determine the direction the pilot should head, we need to consider the effects of the wind on the plane's flight path.
1. Start by drawing a diagram to visualize the situation. Draw a horizontal line to represent the ground, and another line above it to represent the direction and speed of the wind blowing from the south (directly upwards).
2. Since the pilot wants to fly due west, draw another line extending from the ground directly towards the west on your diagram. This line represents the intended direction of the plane's motion.
3. Now, consider the impact of the wind. The wind blows at a speed of 90.0 km/h towards the south. Since the plane's airspeed (speed in still air) is 305.0 km/h, it will be affected by the wind's force.
4. To find the resultant velocity, mentally add the vectors representing the plane's airspeed and the wind speed. Start at the end of the plane's airspeed vector and move in the direction of the wind vector.
5. The magnitude of the resultant vector represents the resulting speed of the plane, while the direction of the resultant vector represents the direction the pilot should head.
In this case, we need to use vector addition to find the resultant vector.
- The airspeed of the plane is 305.0 km/h towards the west.
- The wind speed is 90.0 km/h towards the south.
To combine these vectors, we can use the Pythagorean theorem to find the magnitude of the resultant vector:
Resultant velocity = sqrt((305.0 km/h)^2 + (90.0 km/h)^2)
Calculating this value gives us approximately 318.33 km/h.
Now, to determine the direction in which the pilot should head, we can use trigonometry (specifically, the tangent function):
angle = arctan(90.0 km/h ÷ 305.0 km/h)
Evaluating this expression gives us approximately 16.72 degrees.
Therefore, the pilot should head in a direction 16.72 degrees south of west.