Final answer:
The centripetal force exerted by the control line on a model airplane with a mass of 3.2 kg, moving at a speed of 20 m/s in a circular path with a radius of 12 m, is 106.67 Newtons.
Step-by-step explanation:
The question asks for the centripetal force that the control line exerts on a model airplane to keep it moving in a circular path. Centripetal force can be calculated using the formula F = m × v^2 / r, where m is the mass of the object, v is the velocity, and r is the radius of the circular path. For a model airplane with a mass of 3.2 kg, a speed of 20 m/s, and a circular path radius of 12 m, the centripetal force is given by F = 3.2 kg × (20 m/s)^2 / 12 m.
Plugging the values into the formula, we get:
F = 3.2 kg × 400 m²/s² / 12 m
F = 1280 kg·m/s² / 12 m
F = 106.67 N
Therefore, the force that the control line exerts on the airplane to keep it moving in a circle is 106.67 Newtons.