A bottle lying on the windowsill falls off and takes 4.95 seconds to reach the ground. The distance from the windowsill to the ground is 120.00 meters. Find the time the bottle would take to land if it were to fall the same distance on the moon instead of Earth.

The distance an object falls from rest through gravity is

D = (1/2) (g) (t²)

Distance = (1/2 acceleration of gravity) x (square of the falling time)

We want to see how the time will be affected

if ' D ' doesn't change but ' g ' does.

So I'm going to start by rearranging the equation

to solve for ' t '.

D = (1/2) (g) (t²)

Multiply each side by 2 : 2 D = g t²

Divide each side by ' g ' : 2 D/g = t²

Square root each side: t = √ (2D/g)

Looking at the equation now, we can see what happens

to ' t ' when only ' g ' changes:

- - ' g ' is in the denominator; so bigger 'g' = = > shorter 't'

and smaller 'g' = = > longer 't'.

- - They don't change by the same factor, because 1/g is inside

the square root. So 't' changes the same amount as √1/g does.

Gravity on the surface of the moon is roughly 1/6 the value

of gravity on the surface of the Earth.

So we expect ' t ' to increase by √6 = 2.45 times.

It would take the same bottle (2.45 x 4.95) = 12.12 seconds

to roll off the same window sill and fall 120 meters down to the

surface of the Moon.