Final answer:
The normal force on a 78 kg pilot at the bottom of a dive can be found by calculating the necessary centripetal force for the plane's circular path and subtracting the pilot's weight. However, the calculated value does not match any of the provided options, suggesting a need for verification of values and calculations.
Step-by-step explanation:
To determine the normal force on a 78 kg pilot at the bottom of the dive, we can use the concept of circular motion, where the normal force and the force of gravity together provide the necessary centripetal force for the plane's circular path. The centripetal force (Fc) required for circular motion is given by the equation Fc = mv²/r, where m is the mass of the object, v is the velocity, and r is the radius of curvature.
In the pilot's case, the centripetal force is provided by the sum of the gravitational force (weight) and the normal force exerted by the plane. The weight of the pilot (W) is mg, where g is the acceleration due to gravity (9.8 m/s²). So, W = 78 kg * 9.8 m/s² = 764.4 N. The total force needed for the circular motion is the centripetal force Fc = (78 kg) * (85 m/s)² / (240 m).
Now, Fc = 78 * 7225 / 240 = 2356.25 N. Since the normal force and the gravitational force together must equal the centripetal force, the normal force (Fn) is Fc - W. Therefore, Fn = 2356.25 N - 764.4 N = 1591.85 N.
However, none of the provided options match this value, implying there may have been a mistake in the calculations or in the provided options. Given this discrepancy, we should verify all values and calculations before conclusively determining the normal force.