There is a wind blowing from N80oE at 45 km/h. The airspeed of the plane will be 550 km/h.
(a) What direction should the pilot steer the plane (to whole degree)? Include a diagram as part of your solution.
(b) What will the actual ground speed be of the plane (to one decimal place)?
What direction does the pilot want to go?
To find the direction the pilot should steer the plane and the actual ground speed of the plane, we need to consider the wind's effect on the plane.
(a) Finding the direction for the pilot to steer the plane:
We can find the resulting direction by considering the vectors of the wind and the plane's airspeed.
1. Start by drawing a diagram:
- Draw a line to represent the North direction (N) and mark it.
- From the North direction, measure an angle of 80° East (clockwise) and mark it as N80°E.
- Now draw another line representing the airspeed of the plane starting from N80°E at 550 km/h.
- Finally, draw a vector representing the wind coming from N80°E at 45 km/h.
2. Calculate the resultant vector:
- To find the resultant vector, we need to combine the vectors of the airspeed and the wind:
- Extend the line representing the airspeed of the plane beyond its endpoint.
- From the endpoint of the airspeed vector, draw a line representing the wind vector in the opposite direction.
3. Measure the direction of the resultant vector:
- Use a protractor or ruler to measure the angle between the North direction and the resultant vector.
- This measured angle will tell us the direction the pilot should steer the plane.
(b) Finding the actual ground speed of the plane:
To find the actual ground speed, we need to calculate the magnitude of the resultant vector.
1. Measure the length of the resultant vector on your diagram.
- This length represents the magnitude of the resultant vector, which will be the actual ground speed of the plane.
2. Convert the length to km/h:
- If the length is in cm or any other unit, convert it to km/h using the given scale (1 cm = x km/h).
3. Round the final value to one decimal place:
- This will give us the actual ground speed of the plane.
By following these steps and calculations, you will be able to determine both the direction the pilot should steer the plane and the actual ground speed of the plane.