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

The problem presents a relative motion scenario: the bird's velocity is 10 m/s toward the south relative to the air, and there is a headwind of 2 m/s coming from the south (i.e., the wind is blowing toward the north). To find the bird's velocity relative to the ground, you add the bird's velocity relative to the air to the air's velocity relative to the ground: v_bg = v_ba + v_ag.

- If we assign south as the positive direction, then v_ba = +10 m/s (south), and the headwind v_ag = -2 m/s (since it is toward the north).
- Summing these gives v_bg = (+10) + (-2) = +8 m/s, which means 8 m/s toward the south.

Now evaluate each option:

Option a: 12 m s-1 south. This would occur if you simply added magnitudes without accounting for the direction of the wind, or if you treated the wind as helping the bird rather than opposing it. It ignores the fact that the wind is blowing opposite to the bird’s chosen flight direction, so this overestimates the ground speed.

Option b: -2 m s-1 south. A negative value in the chosen south-positive convention would imply motion toward the north, which contradicts the given directions and misinterprets the vector addition. It essentially treats the wind as if it reversed the bird’s motion entirely, which is not supported by the numbers.

Option c: 8 m s-1 south. This matches the correct vector sum: 10 m/s south relative to air plus 2 m/s north wind results in a net 8 m/s south relative to the ground. It correctly accounts for the opposing wind reducing the bird’s ground speed.

Option d: -12 m s-1 south. This would suggest strong motion toward the north when the data indicate the bird is moving south relative to air and the wind is only 2 m/s. It misapplies the directions and magnitudes, producing an incorrect opposite-direction result.

In summary, the only option consistent with standard relative-motion addition (bird’s velocity relative to air plus wind velocity) is the one yielding 8 m/s toward the south, reflecting the headwind reducing the bird’s ground speed rather than reversing it.

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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