Final answer:
The pilot should set power for the recommended turbulence penetration airspeed and try to maintain a level attitude when unexpectedly encountering a thunderstorm. For dealing with crosswinds when landing, the pilot must calculate and adjust the aircraft heading to compensate for the wind and perform last minute maneuvers for a proper touchdown.
Step-by-step explanation:
If a pilot unintentionally penetrates embedded thunderstorm activity, the recommended procedure is to set power for recommended turbulence penetration airspeed and attempt to maintain a level flight attitude. This involves adjusting power to maintain the aircraft's airspeed recommended for such turbulent conditions which is often higher than normal cruise speed. It is crucial to try to keep the aircraft in a level flight attitude to the greatest extent possible to mitigate the effects of the turbulence.
For the scenario regarding an airplane headed for a runway in a crosswind, let's consider an example where we need to calculate the angle the airplane must fly relative to the air mass. The wind is coming from the northeast at 90 km/h, and the plane's speed relative to the air is 300 km/h. The pilot must account for the crosswind by adjusting the plane's heading. Using vector addition, we can determine the required heading and ground speed.
After calculating the vectors, suppose that the required heading is 10 degrees to the left of north to compensate for the crosswind. Finally, as the plane approaches the runway, the pilot may have to perform last minute maneuvers such as "crabbing" into the wind or making a sideslip to align the plane's wheels with the runway for a safe landing. These adjustments ensure the aircraft lands with minimal side loads on the landing gear.