An air traffic controller tracks an aircraft on its final descent…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
An air traffic controller tracks an aircraft on its final descent. At one moment it is at , and a little later it is at . The coordinates are in kilometres, and the plane is the ground. The aircraft holds a straight path. The controller wants to know where the path reaches the ground, how far the aircraft will fly from to that point, and the angle at which the path meets the ground. The last number is needed to decide if the descent is within the safe limit. Find the -coordinate and the -coordinate of the touchdown point, the distance flown from , and the angle between the path and the ground.
Need a reminder? The key idea
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The line. The direction ratios are , so use . Then , and .
Step 2. Touchdown. gives . So and .
Step 3. The distance flown. The vector has length . For the distance is kilometres.
Step 4. The angle with the ground. The direction cosine along is , so the angle between the path and the ground has . Then .
Answer: , kilometres and .
Check. The height falls by kilometres between and over a path of length kilometres, and gives the same angle.
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