Airline Passenger

You are traveling in an airplane having an airspeed (speed relative to the air-mass it travels in) of 250mph. The airport you are taking off from is 600 miles south of your destination.

  1. How long (to the nearest minute) do you expect your flight will take if there is no wind? (You may omit take-off and landing adjustments).

  2. How about with a wind from the south (blowing northwards) at 50mph?

  3. With a wind from the north at 50mph?

  4. With wind from the south (50mph) for the first 300 miles; and from the north (50mph) for the second 300 miles?

  5. Compare your answers to parts (A) and (D). What does this suggest?

For Homework: Try to prove your hypothesis about the affect of wind ("half" with you, "half" against) on the time of the flight.

  1. The actual forecast is for a 50mph wind from the west (ie eastwards).

    • Assuming the pilot aims the plane so that it heads (i.e., ends up heading) directly towards your destination, how much longer is your trip made by the 50mph wind (versus no wind)?

    • Is it faster to just "aim north", then to "make a left turn" and fly against the wind directly until the destination is reached? How does this "two leg journey" compare, in terms of total flight time, with the previous method?

    • At what angle should the pilot direct the plane?

    • How much longer is your trip going to take with a 100mph wind (versus no wind)?

    • At what angle should the pilot point the plane?

    • What is the velocity vector for the effective velocity of the plane?

    • What is the vector for the air velocity (velocity relative the air mass it is in)?

©Copyleft 1995 by Harel Barzilai. "Share and Enjoy." Inspired by Chapter 8 of Why Math? by R.D. Driver.