This question is also frustrating me. I just don't a single clue how to do it.
A pilot must fly his plane north with a speed of 550 km/hr. A wind of 138 km/hr is blowing at an angle of 31 degrees N of E . What speed does the plane need to keep the desired ground velocity?
To solve this problem, we need to break down the given information into its components and then use vector addition to find the desired ground velocity. Here's how you can do it step by step:
Step 1: Draw a diagram
Start by drawing a simple diagram representing the given situation. Label the plane's velocity as Vp (directed north), the wind's velocity as Vw (directed 31 degrees N of E), and the desired ground velocity as Vg (unknown).
Step 2: Resolve the wind's velocity
Since the wind is blowing at an angle, we need to resolve its velocity into its north and east components. To do this, use trigonometry.
The north component (Vwn) can be calculated as Vw * cos(31°)
The east component (Vwe) can be calculated as Vw * sin(31°)
Step 3: Set up the vector addition
The desired ground velocity (Vg) is the sum of the plane's velocity (Vp) and the wind's velocity components (Vwn and Vwe).
Vg (ground velocity) = Vp (plane velocity) + Vwn (north component of wind velocity) + Vwe (east component of wind velocity)
Step 4: Calculate the ground velocity
Substitute the given values into the equation from step 3 and perform the vector addition to find the magnitude and direction of the ground velocity.
Magnitude:
The magnitude of the ground velocity can be calculated using the Pythagorean theorem:
Magnitude of Vg = √(Vg_north^2 + Vg_east^2)
Direction:
The direction of the ground velocity can be determined using trigonometry:
Direction of Vg = tan^(-1)(Vg_east / Vg_north)
Step 5: Calculate the speed needed
Finally, to find the speed the plane needs to keep the desired ground velocity, simply take the magnitude of the ground velocity calculated in step 4.
The speed needed = Magnitude of Vg
Now you can plug in the given values, perform the calculations, and find the speed the plane needs to keep the desired ground velocity.