Final answer:
To solve this problem, we start by calculating the gravitational force between the federation starship and the shuttlecraft using Newton's law of universal gravitation. Then, we use Newton's second law of motion to calculate the acceleration of the shuttlecraft.
Step-by-step explanation:
To solve this problem, we can start by calculating the gravitational force between the federation starship and the shuttlecraft using Newton's law of universal gravitation: F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Given that the mass of the federation starship is 1.80×10^6 kg, the mass of the shuttlecraft is 2.20×10^4 kg, and the distance between them is 10.0 km (which is equivalent to 10^4 m), we can substitute these values into the formula and calculate the gravitational force between them.
After that, we can use Newton's second law of motion (F = m * a) to calculate the acceleration of the shuttlecraft. The force exerted by the tractor beam on the shuttlecraft is known to be 4.0×10^4 N, and the mass of the shuttlecraft is 2.20×10^4 kg. By substituting these values into the formula, we can calculate the acceleration.