A bird flies with a velocity of 10 m s-1 south encounters a headwind with a speed of 2 m s-1. What is the resultant velocity?

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Question restated: A bird flies with a velocity of 10 m/s south and encounters a headwind with a speed of 2 m/s. What is the resultant velocity?

Option a: 12 m/s south. This would imply the wind is aiding the bird, increasing its speed in the same direction. However, a headwind opposes the bird's motion, not assists it, so this result is inconsistent with the definition of a headwind.

Option b: 8 m/s south. This corresponds to subtracting the headwind speed from the bird’s airspeed when the wind is blowing opposite to the direction of travel (a headwind). Since the bird is moving south and the headwind is effectively blowing north, the wind opposes the motion, reducing the ground speed to 10 − 2 = 8 m/s in the south direction. This is the physically correct resultant velocity.

Option c: -2 m/s south. A negative sign here would imply a reversal of direction or a much larger opposing effect than the given headwind; it does not match the simple vector combination of 10 m/s south with a 2 m/s headwind. It misinterprets the magnitudes and directions, making it an inaccurate representation of the scenario.

Option d: -12 m/s south. This would indicate the bird’s speed has increased in the opposite (north) direction to 12 m/s, which contradicts both the given bird speed and the headwind’s opposing effect. It incorrectly places the resulting velocity in the opposite direction and with a larger magnitude than either component.

Synthesis: In a headwind scenario, the wind opposes the motion, reducing the ground speed along the same direction as the travel. The bird’s airspeed is 10 m/s south, and the headwind adds a 2 m/s component against that motion, yielding a net ground velocity of 10 − 2 = 8 m/s toward the south. Therefore, the correct resultant velocity is 8 m/s south, corresponding to option b.

A bird flies with a velocity of 10 m s-1 south encounters a headwind with a speed of 2 m s-1. What is the resultant velocity?

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