One way to determine the distance to the moon is to bounce a laser beam off a mirror on its surface. How far away is the moon if it takes 2.56 seconds for the laser to "echo" off the moon?
2s=ct
s=ct/2=3•10⁸•2.56/2=3.84•10⁸ m
To determine the distance to the moon using the time it takes for a laser beam to bounce back from its surface, you can use the following steps:
1. Start with the fact that light travels at a speed of approximately 299,792 kilometers per second (km/s) in a vacuum.
2. Divide the total distance traveled by the laser beam (to and from the moon) by the time it took for the "echo" to return. In this case, you have only the time it took for the beam to travel to the moon and back: 2.56 seconds.
3. Since the beam traveled to the moon and back, you need to consider the round trip distance. Divide the time by 2 to get the one-way travel time. In this case, it is 2.56 seconds / 2 = 1.28 seconds.
4. Multiply the one-way travel time by the speed of light to find the distance traveled by the laser beam in that time. In this case, it is 1.28 seconds * 299,792 km/s = 383,535.36 kilometers.
5. Finally, since the distance is the round-trip distance, divide the result by 2 to get the one-way distance from Earth to the moon. In this case, the distance to the moon is 383,535.36 kilometers / 2 = 191,767.68 kilometers.
Therefore, the distance to the moon, based on the given time of 2.56 seconds for the laser beam "echo," is approximately 191,767.68 kilometers.