A pilot points his aircraft due easy, while wind blows from the south. If the resultant velocity of the aircraft is 44m/s 22 degrees [n] of [e], at what speed does the wind blow?
I meant due east
To find the speed at which the wind is blowing, we need to break down the aircraft's velocity into its components: one component due to its own motion (eastward) and the other component due to the wind (southward). We are given the resultant velocity and the direction it is pointing, so we can use trigonometry to solve this problem.
Let's assume the speed of the wind is represented by "w" and the speed of the aircraft (in still air) is represented by "a". We can break down the resultant velocity into its northward and eastward components using the given angle:
Northward component = 44 m/s * sin(22°)
Eastward component = 44 m/s * cos(22°)
Now, since the wind blows from the south, its velocity only affects the northward component of the resultant velocity. Therefore, we can set up the following equation:
Northward component = wind speed * cos(90°)
Plugging in the known values:
44 m/s * sin(22°) = w * cos(90°)
Now, cos(90°) equals zero, so the equation simplifies to:
44 m/s * sin(22°) = 0 * w
This implies that the northward component of the resultant velocity is zero. Therefore, the wind speed is zero. In other words, the wind is not blowing in this scenario.
Please note that in this specific problem, the wind speed turns out to be zero, indicating that there is no wind. However, if the northward component of the resultant velocity was not zero, we could have solved for the wind speed using the above equation.