Final answer:
During a 45 degree banked turn, an airplane weighing 4,500 lbs would need to support approximately 6,700 pounds, which is the closest answer to our calculations based on the lift force formula.
Step-by-step explanation:
During a 45 degree banked turn, an airplane must produce enough lift to support not only its own weight but also provide the necessary centripetal force to maintain the turn. To find the weight the airplane structure would be required to support, we can utilize the formula for the lift force in a banked turn: L = W / cos(θ), where L is the lift force, W is the weight of the airplane, and θ is the banking angle.
For an airplane weighing 4,500 lbs and banking at 45 degrees (cos(45°) = √2/2), the lift force would be calculated as:
L = 4,500 lbs / (√2/2) = 4,500 lbs * √2 ≈ 6,364 lbs.
However, since we are asked for the approximate weight, the closest answer to our calculation is 6,700 pounds, option c. Therefore, during the 45 degree banked turn, the airplane structure would need to support approximately 6,700 pounds to maintain altitude.