A 84.0-kg airplane pilot pulls out of a dive by following, at a constant speed of 163 km/h, the arc of a circle whose radius is 312.0 m.

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To find out the force exerted by the airplane pilot while pulling out of the dive, we can use the concept of centripetal force.

Centripetal force is the force required to keep an object moving in a circular path. It can be calculated using the formula:

Fc = (mv²) / r

Where Fc is the centripetal force, m is the mass of the object, v is the velocity or speed of the object, and r is the radius of the circular path.

In this case, the mass of the airplane pilot is given as 84.0 kg and the speed is given as 163 km/h. We need to convert the speed from km/h to m/s because the formula requires the value of velocity in meters per second.

To convert km/h to m/s, divide the given speed by 3.6:

163 km/h ÷ 3.6 = 45.28 m/s (rounded to two decimal places)

Now we have the mass (m = 84.0 kg), velocity (v = 45.28 m/s), and radius (r = 312.0 m). Substituting these values into the centripetal force formula, we can calculate the force exerted by the pilot:

Fc = (84.0 kg * (45.28 m/s)²) / 312.0 m

= (84.0 kg * 2046.67 m²/s²) / 312.0 m

= 1732.81 Newtons (rounded to two decimal places)

Therefore, the force exerted by the airplane pilot while pulling out of the dive is approximately 1732.81 Newtons.