If a plane takes off on runway 31 (N 31o W) and flies 4 miles, then makes a right (90o) turn and flies 11 miles, what bearing will the traffic controller use to locate the plane?
After making the first leg, the plane is at
(-4sin31°,4cos31°) = (-2.06,3.43)
From there, the plane flies at W31°S,
moving another (-11cos31°,-11sin31°) = (-9.43,-5.67),
ending up at (-11.49,-2.24)
The bearing is W11°S
To determine the bearing that the traffic controller will use to locate the plane, we need to understand the concept of bearing and how it is calculated.
Bearing is the direction or angle measured in degrees that an object, such as an aircraft, is located in relation to a reference point. In aviation, bearings are often measured clockwise from true north.
To calculate the bearing in this scenario, we need to break down the given information step by step:
1. The plane takes off on runway 31, which tells us that the runway is oriented at a heading of 310 degrees clockwise from true north.
2. The plane flies 4 miles in this initial direction, which means it continues along the runway heading of 310 degrees.
3. The plane then makes a right turn of 90 degrees. Since the turn is to the right, we need to add 90 degrees to the previous heading of 310 degrees. This gives us a new heading of 400 degrees.
4. The plane flies 11 miles in this new direction. Therefore, the final bearing will be the new heading after the right turn, which is 400 degrees.
So, to summarize, the traffic controller will use a bearing of 400 degrees to locate the plane.