Final answer:
The bank angle for an airplane during a turn can be calculated using the tangent inverse of the velocity squared over the product of radius and gravity. The perceived weight increase is determined by the ratio of actual weight to the cosine of the bank angle. No specific solution can be provided without more information or clarification.
Step-by-step explanation:
Calculating Bank Angle and Increase in Perceived Weight
To calculate the required bank angle for an airplane making a turn, we can use the relation between the banking angle (θ), speed (v), and radius (r) of the turn, assumed to be an ideally banked turn. The relation is given by θ = tan⁻¹ (v²/rg), where g is the acceleration due to gravity (9.8 m/s²). For the perceived weight increase, we consider the vertical component of the lift force during the banked turn and the horizontal component of the lift force through the center of gravity. The perceived weight is given by W' = W/cos(θ), where W is the actual weight and W' is the perceived weight during the turn.
The bank angle and perceived weight increase have to be calculated through solving these equations with the given speed and time for the turn. Since the problem here does not provide a radius or specific numbers, and has options for answers, I cannot provide a definitive answer without additional information or clarification.