Gravity helps at the tiny airport

Lukla airport in Nepal is one of the strangest in the world. Built to support tourism to the Himalayas, the airport has a single landing runway. What is more, the runway is only 20 m wide, 450 m long, and a 2,800 m cliff at the runway's end, leaving little room for error. In fact, the airport can only be used by so-called Short Takeoff and Landing planes (STOL). Helping somewhat is a 12% incline in the runway from start to finish, so that planes rise through over the course of their deceleration.

Suppose a STOL plane's landing speed is 45 m/s (\approx 100 mph). Neglecting any other effects like wind flaps, or drag, how small will the plane's velocity (in m/s) be at the top of the runway?

Details

  • The runway itself is 450 m long, i.e. if you walked from the bottom to the top, you'd walk 450 m along the runway.
  • An ff% incline means that if you walk a distance dd along an incline, your rise is given by fd/100fd/100.
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