Final answer:
You may elect to take off with a higher speed than normal when dealing with a heavy aircraft. This is required to generate adequate lift for takeoff due to the increased weight. Other scenarios mentioned do not typically involve the intentional choice of higher takeoff speeds.
Step-by-step explanation:
When considering when you may elect to take off with a higher speed than normal, the correct situation would be when dealing with a heavy aircraft. This is because a heavier aircraft requires more speed to generate adequate lift for takeoff. It's not typical to choose a higher speed intentionally during crosswind conditions, during a short-field takeoff, or when operating at high elevations. In fact, during crosswind conditions, you generally want to maintain control at the lowest practical speed, and during a short-field takeoff, you might use high lift devices to enable lift at a lower speed. When operating at high elevations, performance is degraded due to thinner air, and while taking off at a higher ground speed might be necessary due to the lower air density, it's not a voluntary 'election' but a requirement of the conditions.
Taking off into the wind is preferable because it helps generate more lift as the aircraft has a higher airspeed relative to the ground, which is important for achieving flight. This is related to Bernoulli's principle, where the increased velocity over the wing's upper surface results in a pressure decrease and thus lift. The same principle explains why an aircraft might need more speed to compensate for the reduced air density at high elevations or to achieve the required lift when heavier than usual.