In this scenario, we explore the concept of using a spacecraft equipped with reflective sails to harness sunlight for propulsion, a promising technology for low-cost space travel. The spacecraft, a 400-kilogram satellite, utilizes its reflective sails to capture sunlight, generating a force known as radiation pressure. This force propels the satellite forward, allowing it to gain speed without relying on traditional fuel sources.

The total area of the reflective sails is crucial for calculating the force exerted on the satellite. Each sail has an area of 5,000 square meters, and with two sails, the total area becomes 10,000 square meters. The intensity of sunlight at the satellite's location is approximately 1350 W/m². For reflective surfaces, the force due to radiation pressure can be calculated using the formula:

F_{\text{reflected}} = \frac{2 \cdot I \cdot A}{c}

Here, I represents the intensity of sunlight, A is the total area of the sails, and c is the speed of light, approximately \(3 \times 10^8\) m/s. Plugging in the values:

F_{\text{reflected}} = \frac{2 \cdot 1350 \, \text{W/m}^2 \cdot 10,000 \, \text{m}^2}{3 \times 10^8 \, \text{m/s}} \approx 0.09 \, \text{N}

This force, while small, is constant and will continue to accelerate the satellite over time. To determine the satellite's velocity after one year, we apply kinematic equations. Assuming the satellite starts from rest, the initial velocity (\(v_0\)) is 0. The acceleration (\(a\)) can be calculated using Newton's second law:

a = \frac{F}{m} = \frac{0.09 \, \text{N}}{400 \, \text{kg}} = 2.25 \times 10^{-4} \, \text{m/s}^2

Next, we convert one year into seconds for our calculations:

t = 1 \, \text{year} = 365 \, \text{days} \times 24 \, \text{hours/day} \times 60 \, \text{minutes/hour} \times 60 \, \text{seconds/minute} \approx 31,536,000 \, \text{seconds}

Now, we can find the final velocity (\(v_f\)) using the formula:

v_f = v_0 + a \cdot t = 0 + (2.25 \times 10^{-4} \, \text{m/s}^2) \cdot (31,536,000 \, \text{s}) \approx 7,100 \, \text{m/s}

This calculation illustrates that even a small force can lead to significant changes in velocity over extended periods, demonstrating the potential of solar sails for long-duration space missions. The satellite, propelled by sunlight, could achieve impressive speeds as it travels through the solar system.