PHYSICS HIGH SCHOOL

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.

Answers

Answer 1
Answer:

The time of the bottle would take to land if it were to fall the same distance on the moon instead of Earth is 12.12 seconds.

To find the Time, the given values are,

A bottle lying on the windowsill fall = 4.95 seconds

The distance of the object to the ground = 120 meters

What is the distance of the object?

The distance d an object falls under the influence of gravity is determined by the equation

                        D  =  (1/2) (g) (t²)

where,

D - Distance

g - acceleration of gravity

t²- square of the falling time

In the equation,

Multiply each side by  2 : 2 D = gt²

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

Square root each side: t = √ (2D/g)

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 Earth.

Thus, the time of the bottle would take to land if it were to fall the same distance on the moon instead of Earth is 12.12 seconds.

Learn more about object fall due to the gravity,

brainly.com/question/9476165

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Answer 2
Answer:
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.

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