Question

In 1969 the Apollo astronauts left a laser reflector on the Moon. This was to be used to help scientists to make very accurate measurements of the distance between the Earth and the Moon. The mean distance between the centres of the Earth and Moon is 385 000 km, and light travels at 3 × 10⁸ m/s.

Answer 1

I guess that you want to calculate the averae time that passes since you "fire" the laser, and you see the reflection.

We know that:

Distance = Time*Speed

Distance/speed = time.

In this case we have:

Distance = 385,000km

Speed = 3x10^8m/s

First, there are two corrections:

1) The distance to the moon is traveled two times, so the actual distance would be:

Distance = 2*385,000km = 770,000km

2) Both quantities should be written in the same units, so we can write the speed in kilometers:

We know that:

1km = 1000m

Then 3x10^8 m/s = (3x10^8/10^3) km/s = 3x10^(8 - 3) km/s = 3x10^5 km/s

Now we can solve the equation:

Time = 770,000km/(300,000 km/s) = 2.57 seconds.