Question

Unreasonable Results A commercial airplane has an air speed of 280 m/s due east and flies with a strong tailwind. It travels 3000 km in a direction 5º south of east in 1.50 h.

(a) What was the velocity of the plane relative to the ground?
(b) Calculate the magnitude and direction of the tailwind’s velocity.
(c) What is unreasonable about both of these velocities?
(d) Which premise is unreasonable?

The velocity of the plane relative to the ground is approximately:

a) 250 m/s
b) 280 m/s
c) 310 m/s
d) 340 m/s

Answer 1

To find the velocity of the plane relative to the ground, combine the airspeed and tailwind velocity. The tailwind's magnitude and direction can be calculated by subtracting the airspeed from the velocity relative to the ground. Both velocities are unreasonable because they exceed the maximum typical airspeed of a commercial airplane.

Step-by-step explanation:

To find the velocity of the plane relative to the ground, we need to combine the plane's airspeed and the velocity of the tailwind. Using vector addition, we can calculate that the velocity of the plane relative to the ground is approximately 310 m/s, in a direction 5° south of east.

To calculate the magnitude and direction of the tailwind's velocity, we subtract the plane's airspeed from its velocity relative to the ground. This gives us a magnitude of approximately 30 m/s, in a direction opposite to the plane's heading, or 185°.

Both velocities are unreasonable because they exceed the maximum typical airspeed of a commercial airplane, which is usually around 900 km/h. The premise that an airplane can travel at an airspeed of 280 m/s is unreasonable.

The primary topic of this question is calculating velocities using vector addition.