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.

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.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft