Final answer:
The correct action is to re-plan the journey to avoid the mountain pass because the calculated density altitude exceeds the aircraft's service ceiling, which makes flying through the pass unsafe.
Step-by-step explanation:
The correct action to take when encountering a density altitude that exceeds the service ceiling of your aircraft is to avoid flying in those conditions. In this scenario, with a calculated density altitude of the mountain pass at 14,800' MSL and an aircraft service ceiling of 14,000' MSL, flying through the pass is not advisable because the plane may not be capable of sufficient climb performance to safely navigate the pass. Instead, re-planning your journey to avoid the mountain pass is the safest action (option a).
The concept of density altitude is important as it affects the performance of an airplane across all phases of flight, not just for takeoff. As the altitude increases, air density decreases, which can lead to significantly poorer aircraft performance. This concept is visually represented in Figure A4 Altitude-Air Density Relationship, where we see that air density decreases with increasing altitude.
Option b is incorrect as density altitude affects not just takeoff but overall aircraft performance. Option c is incorrect because relying on mountain thermals is unpredictable and does not guarantee safe climb performance. Option d, to cancel the flight, could be considered if no alternative route is possible and avoiding the mountain pass would not make the flight viable.