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

Velocities are vectors and add algebraically; a headwind opposes the bird’s motion, so it reduces the bird’s resultant (ground) speed.

1) Relevant knowledge points and concepts
- Velocity has magnitude and direction and must be added vectorially. 
- A headwind is wind blowing opposite to the direction of travel, so its velocity vector is opposite the bird’s flight vector. 
- Use a sign convention (choose south as positive or north as positive) and add components.

2) Step-by-step reasoning (using south as positive)
- Bird’s velocity = +10 m s^-1 (south).
- Headwind: since it opposes the bird, it is directed north = −2 m s^-1 (if south is positive).
- Resultant velocity = bird’s velocity + wind velocity.

3) Calculations (intermediate steps shown)
- Resultant = (+10 m s^-1) + (−2 m s^-1) = +8 m s^-1.
- Positive sign corresponds to south, so resultant = 8 m s^-1 south.

(If instead you choose north as positive: bird = −10 m s^-1, wind = +2 m s^-1, sum = −8 m s^-1 → 8 m s^-1 south. Both conventions give the same physical result.)

4) Why the correct answer is correct
- The headwind subtracts from the bird’s southward velocity by 2 m s^-1, reducing the ground speed from 10 to 8 m s^-1 while preserving the southward direction.

5) Why the other options are incorrect
- a. −12 m s^-1 south implies 12 m s^-1 opposite sign confusion (would mean 12 m s^-1 north or incorrectly adding the wind in the same direction).  
- b. 12 m s^-1 south treats the wind as a tailwind (adding 2 m s^-1), which is wrong for a headwind.  
- d. −2 m s^-1 south would indicate a net 2 m s^-1 northward motion, which contradicts the larger southward bird speed.

6) Conclusion
- The resultant velocity is 8 m s^-1 south, matching the provided correct answer: c. 8 m s^-1 south.

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?Single choice

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