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 is followed by a 2,800 m cliff, 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, that planes rise through over the course of their deceleration.
Suppose a STOL plane's landing speed is 45 m/s (\(\approx\) 100 mph). In addition to gravity, the plane experiences a first order drag force \(F_d = -kv\).
How close (in meters) does the plane get to the end of the runway?
- \(k = 20\) N\(\cdot\)s/m
- \(g=9.81\) m/s (Important!)
- The plane's mass is 500 kg
- 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 \(f\)% incline means that if you walk a distance \(d\) along an incline, your rise is given by \(fd\).