Final answer:
The force the ship exerts on the pilot is 87 N, equal and opposite to the force the pilot exerts on the ship. The pilot's acceleration is 8.29 m/s², calculated using the ratio of force to the pilot's mass. The ship's acceleration is 0.08 m/s², calculated by dividing the force by the ship's mass.
Step-by-step explanation:
The question involves understanding the concept of action-reaction forces and the motion of objects under the influence of those forces, a fundamental topic in physics. When the turtle pilot exerts a force on the spaceship (and conversely, the ship on the pilot), we can apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Therefore, the force that the ship exerts on the pilot (a) is equal to the force exerted by the pilot on the ship.
a. The force that the ship exerts on the pilot is 87 N (Option A), which is equal in magnitude and opposite in direction to the force exerted by the pilot on the ship, according to Newton's third law.
b. To calculate the acceleration of the pilot, we use Newton's second law of motion, which states that force equals mass times acceleration (F = ma). So, the pilot's acceleration (a) is given by:
a = F / m
a = 87 N / 10.5 kg
a = 8.29 m/s²
Therefore, the pilot's acceleration is 8.29 m/s² (Option A).
c. Similarly, the acceleration of the ship is calculated using the same formula :
a = F / m
a = 87 N / 1,085 kg
a = 0.08 m/s²
The acceleration of the ship is 0.08 m/s² (Option A).