Final answer:
The Gimli Glider incident involves physics principles related to deceleration and gliding, while constructing a problem about landing in a crosswind involves vector physics and trigonometry.
Step-by-step explanation:
Engine Failure and Airplane Landing Dynamics
The scenario described involves a Boeing 767, famously known as the Gimli Glider, which faced an engine failure due to fuel miscalculation. The physics principles in play here revolve around the airplane's acceleration during landing and the role of gliding without engine power.
When an airplane lands on a runway traveling east and comes to a stop, it undergoes negative acceleration or deceleration. This is because it is slowing down, which means that the acceleration vector is directed opposite to the velocity vector. The rate of this deceleration would depend on various factors such as the runway's friction, airplane's weight, and reverse thrust applied by the engines if available.
The construction of a problem involving an airplane landing with a crosswind deals with vector addition to determine the necessary heading to maintain a velocity parallel to the runway. The speed of the airplane relative to the ground is found by adding the velocity vectors of the airplane relative to the wind and the wind speed and direction itself. This type of calculation involves both trigonometry and vector physics.
Last minute maneuvers by pilots, such as the crab angle correction, would be essential to align the airplane wheels with the runway upon touchdown in crosswind situations. This ensures the safety and stability of the landing process.