A company called Amazedrone is developing a system to deliver packages using a drone from warehouse...

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A company called Amazedrone is developing a system to deliver packages using a drone from warehouse A to staging area B. Key to the success is the how quickly the drone can fly from A to B and return to A, called an out-and-return flight. Someone brings up the question of whether a headwind will slow down the operation because of increased out-and-return flight time. One manager thinks there will be absolutely no effect because a headwind that slows down the out leg will become a tailwind that speeds up the craft in the return leg. The team tasks you to figure this out. Assume that the drone flies at a constant airspeed, V. Let the headwind speed be W, and the distance from A to B be d. Do the following: (i) Derive the expression for the time for the out flight from A to B. (ii) Derive the expression for the time for the return flight from B to A. (iii) Calculate expression for the total time. (iv) Find the headwind that will result in the minimum total time. A company called Amazedrone is developing a system to deliver packages using a drone from warehouse A to staging area B. Key to the success is the how quickly the drone can fly from A to B and return to A, called an out-and-return flight. Someone brings up the question of whether a headwind will slow down the operation because of increased out-and-return flight time. One manager thinks there will be absolutely no effect because a headwind that slows down the out leg will become a tailwind that speeds up the craft in the return leg. The team tasks you to figure this out. Assume that the drone flies at a constant airspeed, V. Let the headwind speed be W, and the distance from A to B be d. Do the following: (i) Derive the expression for the time for the out flight from A to B. (ii) Derive the expression for the time for the return flight from B to A. (iii) Calculate expression for the total time. (iv) Find the headwind that will result in the minimum total time.