A seagull flies at a velocity of 10.00 m/s straight into the wind.
(a) If it takes the bird 18.0 min to travel 6.00 km relative to the earth, what is the velocity of the wind?
d = (Vs-Vw)t = 6000 m.
(10-Vw)1080s = 6000
10800-1080Vw = 6000
1080Vw = 10,800-6000 = 4800
Vw = 4.444 m/s.
Oh, I see we have a bird-brain problem here! So, we have a seagull flying against the wind, trying to prove that birds can be superheroes too. Let's see if we can help this avian avenger.
First of all, we need to convert the time from minutes to seconds because physics doesn't have time for minutes. It's more of a "now" kind of subject. So, 18.0 minutes is equal to 1080 seconds.
Now, we know that velocity is distance over time. But because the seagull is flying against the wind, its speed will be a bit slower than it would be in still air. Let's call the speed of the wind "w".
We can write an equation: velocity of the bird = velocity relative to the earth + velocity of the wind.
The velocity relative to the earth is the speed of the bird minus the speed of the wind: 10.00 m/s - w.
And the distance traveled is the velocity relative to the earth multiplied by time: (10.00 m/s - w) * 1080 s = 6.00 km.
Now we need to convert the distance to meters because the metric system is the ruler of physics. So 6.00 km is equal to 6000 m.
Now we can solve for the velocity of the wind, but we'll leave that to the nerdy math bot. I'm just here to make you laugh, not do calculations!
To solve this problem, we can use the formula: velocity = distance / time.
Given:
Velocity of the seagull, v = 10.00 m/s.
Time taken by the seagull, t = 18.0 minutes = 18.0 * 60 seconds = 1080 seconds.
Distance covered by the seagull, d = 6.00 km = 6.00 * 1000 m = 6000 m.
Let's calculate the velocity of the wind.
Step 1: Calculate the velocity of the seagull relative to the earth.
Velocity of the seagull, v = distance / time.
v = 6000 m / 1080 s = 5.56 m/s.
Step 2: Calculate the velocity of the wind.
Velocity of the wind, w = velocity of the seagull - velocity of the seagull relative to the earth.
w = 10.00 m/s - 5.56 m/s = 4.44 m/s.
Therefore, the velocity of the wind is 4.44 m/s.
To find the velocity of the wind, let's go step by step:
Step 1: Convert minutes to seconds
We need to convert the time of 18.0 minutes into seconds. Since there are 60 seconds in a minute, we multiply 18.0 minutes by 60 to get the equivalent time in seconds:
18.0 min * 60 s/min = 1080 s
Step 2: Convert kilometers to meters
We need to convert the distance of 6.00 km into meters. Since there are 1000 meters in a kilometer, we multiply 6.00 km by 1000 to get the equivalent distance in meters:
6.00 km * 1000 m/km = 6000 m
Step 3: Calculate the average velocity
The average velocity can be calculated by dividing the distance traveled (6000 m) by the time taken (1080 s):
Average velocity = Distance / Time
Average velocity = 6000 m / 1080 s
Step 4: Subtract the velocity of the wind
Let's assume that the velocity of the wind is v_wind. Since the bird is flying straight into the wind, the relative velocity of the bird with respect to the Earth's frame of reference is equal to the bird's velocity minus the wind's velocity:
Relative velocity = Bird's velocity - Wind's velocity
Given that the bird's velocity is 10.00 m/s, the equation becomes:
Relative velocity = 10.00 m/s - v_wind
Step 5: Set up the equation
The relative velocity is equal to the average velocity (calculated in Step 3):
Relative velocity = Average velocity
Substituting the values:
10.00 m/s - v_wind = 6000 m / 1080 s
Step 6: Solve for v_wind
Now we need to solve the equation for the velocity of the wind, v_wind. We can rearrange the equation as follows:
v_wind = 10.00 m/s - (6000 m / 1080 s)
Calculate the right side of the equation:
v_wind ≈ 10.00 m/s - 5.56 m/s
v_wind ≈ 4.44 m/s
Therefore, the velocity of the wind is approximately 4.44 m/s.