1. **State the problem:** We need to find the net external force exerted on a 1400-kg artillery shell that is accelerated at $2.60 \times 10^{1}$ m/s$^2$. 2. **Formula used:** Newton's second law states that force is mass times acceleration: $$F = ma$$ where $F$ is the force in newtons (N), $m$ is the mass in kilograms (kg), and $a$ is the acceleration in meters per second squared (m/s$^2$). 3. **Calculate the force on the shell:** Given: $$m = 1400 \text{ kg}$$ $$a = 2.60 \times 10^{1} = 26.0 \text{ m/s}^2$$ Calculate: $$F = 1400 \times 26.0$$ $$F = 36400 \text{ N}$$ 4. **Force exerted on the ship by the shell:** By Newton's third law, the force exerted on the ship by the shell is equal in magnitude and opposite in direction to the force exerted on the shell by the ship. Therefore, the magnitude of the force on the ship is also: $$36400 \text{ N}$$ **Final answers:** - Net external force on the shell: $36400$ N - Magnitude of force on the ship: $36400$ N