Final answer:
The velocity of the wind is approximately 1.5 m/s. It will take approximately 34 minutes for the bird to return 6.00 km. The wind affects the total round-trip time, making it longer when flying against the wind and shorter when flying with the wind.
Step-by-step explanation:
To find the velocity of the wind, we can use the equation:
Velocity of the bird = Velocity of the bird relative to the earth + Velocity of the wind
Given that the velocity of the bird relative to the earth is 9.00 m/s and the bird takes 20.0 min (or 1200 s) to travel 6.00 km, we can calculate the velocity of the wind.
To do this, we can use the formula:
Distance = Velocity x Time
So, 6.00 km = (9.00 m/s + Velocity of the wind) x 1200 s
Simplifying this equation, we find that the velocity of the wind is approximately 1.5 m/s.
(b) When the bird turns around and flies with the wind, its velocity relative to the earth is the sum of its velocity in still air and the velocity of the wind. So, the bird's velocity relative to the earth is 9.00 m/s + 1.5 m/s = 10.5 m/s. To calculate how long it will take the bird to return 6.00 km, we can use the formula:
Time = Distance / Velocity
Therefore, the time it will take the bird to return 6.00 km is (6.00 km) / (10.5 m/s) = 0.57 hours, or approximately 34 minutes.
(c) When the bird is flying against the wind, it takes longer to travel the same distance compared to flying in still air. This is because the wind slows down the bird's velocity relative to the earth. On the other hand, when the bird is flying with the wind, it takes less time to travel the same distance compared to flying in still air. This is because the wind helps to increase the bird's velocity relative to the earth.