Final answer:
To reach the Moon, a spaceship must reach an escape velocity of about 11 kilometers per second. Given an acceleration of 20 m/s² over 2 minutes, the spaceship's final velocity would be 2400 m/s, assuming it started from rest, which contradicts the 1000 km covered distance. Escape velocity is essential for spacecraft to leave Earth's orbit and coast towards the Moon.
Step-by-step explanation:
Understanding the Speed Required to Reach the Moon
To determine the initial and final velocities of a spaceship on its way to the Moon, one must consider the spacecraft's acceleration and the distance covered during the acceleration. Given that a spaceship accelerates at 20 m/s² for 2 minutes (120 seconds), we can employ kinematic equations to calculate the velocities. Using the equation for constant acceleration, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Assuming an initial velocity u of 0 (since it just left Earth's orbit), the final velocity v would be a * t = 20 m/s² * 120 s = 2400 m/s.
The distance covered can also be calculated using the kinematic equation s = ut + 1/2at², where s is the displacement. As we've assumed an initial velocity u of 0, the equation simplifies to s = 1/2at². By substituting the given values, we get the distance s = 1/2 * 20 m/s² * (120 s)² = 144,000 m = 144 km, which is not consistent with the 1000 km distance provided. This suggests that there might be an error in the given values or that the spaceship had an initial velocity before the acceleration began.
The speed to reach interplanetary targets like the Moon involves achieving escape velocity, which is approximately 11 kilometers per second (25,000 miles per hour). Once escape velocity is reached and the spacecraft leaves Earth's orbit, it generally coasts to the Moon without further acceleration.