A seagull flies at a velocity of 7.00 m/s straight into the wind.
(a) If it takes the bird 17.0 min to travel 6.00 km relative to the earth, what is the velocity of the wind?
(b) If the bird turns around and flies with the wind, how long will he take to return 6.00 km?
A dog running in an open field has components of velocity
v
x
= 2.7
m/s
and
v
y
= -1.7
m/s
at time
t
1
= 11.8
s
. For the time interval from
t
1
= 11.8
s
to
t
2
= 22.6
s
, the average acceleration of the dog has magnitude 0.49
m/
s
2
and direction 35.5
∘
measured from the
+x−axis
toward the
+y−axis
To solve these questions, we'll use the concept of relative velocity. Let's go ahead and solve each question step by step:
(a) To find the velocity of the wind, we need to consider that when the bird is flying against the wind, its actual velocity is the sum of its velocity relative to the wind and the velocity of the wind. Therefore, we have the equation:
Actual velocity of the bird = Velocity of the wind + Velocity of the bird relative to the wind
Given that the velocity of the bird relative to the wind is 7.00 m/s (since it flies straight into the wind), we can rewrite the equation as:
Actual velocity of the bird = Velocity of the wind + 7.00 m/s
Now, let's convert the 17.0 minutes into seconds for consistency:
Time = 17.0 minutes = 17.0 * 60 = 1020 seconds
The distance traveled by the bird relative to the earth is given as 6.00 km. So, we can use the formula:
Distance = Velocity * Time
To find the actual velocity of the bird, we can rearrange the formula as:
Velocity = Distance / Time
Substituting the values, we have:
Actual velocity of the bird = 6.00 km / 1020 s
But we need to convert the distance and time to meters and seconds respectively, since we're working with the SI units. 1 km = 1000 m, so the actual distance is 6000 m.
Actual velocity of the bird = 6000 m / 1020 s
Simplifying the equation:
Actual velocity of the bird = 5.88 m/s
Now, we can substitute this value into our initial equation:
5.88 m/s = Velocity of the wind + 7.00 m/s
Rearranging the equation to solve for the velocity of the wind:
Velocity of the wind = 5.88 m/s - 7.00 m/s
Calculating the velocity of the wind:
Velocity of the wind = -1.12 m/s
Therefore, the velocity of the wind is -1.12 m/s (negative sign means it is blowing against the direction of the bird's flight).
(b) When the bird turns around and flies with the wind, its actual velocity will be the difference between the velocity of the bird relative to the wind and the velocity of the wind. So, we have the equation:
Actual velocity of the bird = Velocity of the bird relative to the wind - Velocity of the wind
Given that the velocity of the bird relative to the wind is 7.00 m/s (since it flies with the wind), we can rewrite the equation as:
Actual velocity of the bird = 7.00 m/s - Velocity of the wind
Since the bird is flying with the wind, the relative velocity is the same as the actual velocity:
Actual velocity of the bird = 7.00 m/s
Using the formula Distance = Velocity * Time, we can solve for the time it takes for the bird to return 6.00 km:
Time = Distance / Velocity
Substituting the values:
Time = 6.00 km / 7.00 m/s
Again, we need to convert the distance to meters:
Time = 6000 m / 7.00 m/s
Simplifying the equation:
Time = 857.14 s
Therefore, it will take the bird approximately 857.14 seconds (or 14.29 minutes) to return 6.00 km when flying with the wind.
Please note that the above calculations assume a constant velocity of the wind and do not take into account other factors such as air resistance.