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?

Question

BlackTom AI · Accepted Answer

Velocity vectors add: v_resultant = v_bird + v_wind.

1. Relevant concepts
- Velocity is a vector (magnitude and direction). When a bird flies through moving air, the bird’s ground velocity is the vector sum of its airspeed (velocity relative to the air) and the wind velocity (velocity of air relative to the ground).
- A headwind blows opposite to the bird’s direction of travel, so it reduces the bird’s ground speed.

2. Step-by-step reasoning
- Take south as the positive direction. The bird’s velocity is v_bird = +10 m s^-1 (south).
- The headwind blows toward the north at 2 m s^-1, which is opposite south, so represent it as v_wind = −2 m s^-1 (south sign convention).
- Add the vectors: v_resultant = v_bird + v_wind.

3. Intermediate calculation
- v_resultant = (+10 m s^-1) + (−2 m s^-1) = +8 m s^-1.

4. Why this answer is correct
- The positive sign (+8) with our chosen convention means the resultant is 8 m s^-1 toward the south. Physically, the 2 m s^-1 headwind subtracts from the bird’s 10 m s^-1 southward speed, leaving 8 m s^-1 south as the ground velocity.

5. Why the other options are incorrect
- a. −12 m s^-1 south would correspond to 12 m s^-1 north (opposite direction) — not supported by the given magnitudes; a headwind cannot reverse and increase the bird’s speed.
- b. −2 m s^-1 south corresponds to 2 m s^-1 north (bird moving north), which is incorrect — the bird still moves south overall.
- c. 12 m s^-1 south implies the wind added speed (a tailwind), but the problem states a headwind; thus the speed should decrease, not increase.

6. Conclusion
- The resultant ground velocity is 8 m s^-1 south, which matches option d.

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?单项选择题

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