To solve this problem, we need to determine the net force acting on the spaceship using Newton's Second Law of Motion and then calculate the force exerted by the spaceship's engine.

The formula for net force is:

$F_{\text{net}} = ma$

Where:

• $m$ is the mass of the spaceship (1300 kg),
• $a$ is the acceleration of the spaceship (0.5 m/s$^2$).

The net force required to produce the acceleration is:

$F_{\text{net}} = 1300 \times 0.5 = 650 \, \text{N}.$

Now, the engine force ($F_{\text{engine}}$) must overcome both the net force and the opposing force from the meteor shower ($F_{\text{meteor}}$):

$F_{\text{engine}} = F_{\text{net}} + F_{\text{meteor}}.$

Substituting the values: $F_{\text{engine}} = 650 + 500 = 1150 \, \text{N}.$

Final Answer:

The engine exerts a force of 1150 N on the spaceship.

Further Questions for Exploration:

1. What would happen to the required engine force if the mass of the spaceship were doubled?
2. How would the acceleration change if the meteor shower exerted a larger opposing force?
3. If the engine produced only 500 N of force, what would the resulting acceleration be?
4. How long would it take for the spaceship to reach a velocity of 100 m/s under these conditions?
5. Can you calculate the work done by the engine force after traveling a distance of 200 meters?

Tip: Always account for opposing forces when calculating net force in real-world scenarios!