An airplane of mass 1.30 104 kg is moving at 52.0 m/s. The pilot then increases the engine's thrust to 7.00 104 N. The resistive force exerted by air on the airplane has a magnitude of 3.00 104 N.
a = F/m = (7-3) * 10^4 / (1.3*10^5)
To find the acceleration of the airplane after the pilot increases the engine's thrust, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
Net force = mass * acceleration
In this case, the net force is the difference between the thrust force and the resistive force exerted by the air:
Net force = thrust force - resistive force
Given that the mass of the airplane is 1.30 * 10^4 kg, the thrust force is 7.00 * 10^4 N, and the resistive force is 3.00 * 10^4 N, we can calculate the net force:
Net force = 7.00 * 10^4 N - 3.00 * 10^4 N = 4.00 * 10^4 N
Now we can solve for the acceleration:
acceleration = Net force / mass = (4.00 * 10^4 N) / (1.30 * 10^4 kg) = 3.08 m/s^2
Therefore, the acceleration of the airplane after the pilot increases the engine's thrust is 3.08 m/s^2.