Final answer:
It took NASA astronauts 111 hours to reach the Moon with an average speed of 0.961 km/s. The distance to the Moon based on the speed of an electromagnetic signal is 3.84×10^5 km.
Step-by-step explanation:
The student asked two questions related to the Apollo missions to the Moon, allowing us to calculate travel time and average speed using the given distance, as well as identify the correct distance value based on the speed of electromagnetic waves (light or radio waves).
To calculate the time it took to reach the Moon in hours, we start with the given duration of the trip, which is 4.625 days. Since there are 24 hours in a day, we multiply:
4.625 days × 24 hours/day = 111 hours.
To calculate the average speed of the astronauts on their trip to the Moon, we divide the distance by the time taken. First, we convert the time into seconds (since speed is typically in km/s or m/s):
111 hours × 3600 seconds/hour = 399600 seconds.
Now, we divide the distance by the time:
3.84 × 105 km / 399600 seconds = 0.961 km/s average speed.
An astronaut on the Moon receives a message from Earth, sent by electromagnetic radiation, which takes 1.28 seconds to travel. Given the speed of light in a vacuum is about 3×108 meters per second, multiplying 1.28 seconds by this speed gives us the one-way distance to the Moon:
Speed of light × Time = Distance
3×108 m/s × 1.28 s = 3.84×108 meters, which is equivalent to 3.84×105 kilometers. The correct answer is therefore (c) 3.84×105 km.