Question

An airplane with an airspeed of 850 km/hr encounters a northwest wind at 100 km/hr. What angle (in degrees) should the pilot fly to head due north?

a) 15.5°
b) 20.7°
c) 25.9°
d) 30.2°

Answer 1

To determine the angle, calculate the net velocity by finding the horizontal and vertical components of the airspeed and wind velocity using trigonometry. Finally, use the tangent function to find the angle. Therefore, the correct option is a) 15.5°.

Step-by-step explanation:

To determine the angle at which the pilot should fly to head due north, we need to find the net velocity of the plane. The net velocity is the vector sum of the airspeed and the wind velocity. We can break down the velocities into their horizontal and vertical components, where the horizontal components are affected by the wind and the vertical components remain the same.

Let's calculate the horizontal and vertical components using trigonometry:

• Horizontal component of airspeed: 850 km/hr * cos(45°)
• The vertical component of airspeed: 850 km/hr * sin(45°)
• The horizontal component of wind velocity: 100 km/hr * cos(135°)
• The vertical component of wind velocity: 100 km/hr * sin(135°)

Now, we can calculate the horizontal and vertical components of the net velocity by adding the corresponding airspeed and wind velocity components:

• Horizontal component of net velocity: (airspeed horizontal component) + (wind velocity horizontal component)
• Vertical component of net velocity: (airspeed vertical component) + (wind velocity vertical component)

Finally, we can find the angle using the tangent function:

• Angle = arctan(vertical component of net velocity / horizontal component of net velocity)

Calculating all the values gives us an angle of approximately 15.5°.

Therefore, the correct option is a) 15.5°.