Final answer:
Anton Chekhov's play commonly known as The Seagull is correctly titled The Seagull. For the physics problem, the velocity of the wind is calculated to be 4 m/s when a seagull flies at a velocity of 9 m/s into it. The effect of the wind on the round-trip time is that it causes longer travel time against the wind and shorter with it.
Step-by-step explanation:
The title of Anton Chekhov's play commonly known as The Seagull is indeed c) The Seagull. However, the question seems to be a mix-up between a literature question and a physics problem. To address the physics component:
Velocity of the Wind
(a) If a seagull flies at a velocity of 9.00 m/s straight into the wind and it takes the bird 20.0 minutes to travel 6.00 km relative to the Earth, we need to calculate the wind's velocity. The seagull's airspeed (without wind) and groundspeed (with wind) are different due to the wind's influence. To find the wind's velocity, we can set up an equation comparing the airspeed and groundspeed. Since it took 20 minutes (1200 seconds) to travel 6 km (6000 meters), the groundspeed is 6000 meters / 1200 seconds = 5 m/s. The difference between the airspeed and the groundspeed yields the wind's velocity: 9 m/s - 5 m/s = 4 m/s. Therefore, the wind's velocity is 4 m/s.
Time to Return
(b) When the bird turns around and flies with the wind, its groundspeed is the sum of its airspeed and the wind's velocity: 9 m/s + 4 m/s = 13 m/s. To calculate how long it will take to return 6 km, we use the formula time = distance/speed. Here, time = 6000 meters / 13 m/s = approximately 461.54 seconds, or about 7.69 minutes.
Effect of Wind on Round-trip Time
(c) The wind affects the total round-trip time compared to what it would be with no wind by causing the seagull to take longer to travel against the wind and quicker when flying with the wind. The variations in travel time for each leg of the trip mean that the total time with wind will differ from the time it would take in calm conditions, generally taking longer when there's a headwind and less time with a tailwind.