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. (Note: Acceleration due to gravity on the moon is 1/6 that on Earth.)

Question

OLIVER69 · Answer

For earth
h=ut+.5*g*t^2
Given
u=0
h=120m
t=4.95sec
g=?

For moon
h=ut+.5*gt^2
Given
h=120m
u=0
t=?

$$g (earth) = 9.81_{m/s^2}$$

$$g (moon) = 9.81×\frac{ 1 }{ 6 }=1.62_{m/s^2}$$

$$y _{f}=y _{i}+v _{i}×t+\frac{ at^2 }{ 2 }$$

$$0=120+0×t+\frac{ (1.62)t^2 }{ 2 }$$

t=12.171612, −12.171612

rounded your answer is $$\pm 12.2$$

(hopes it makes sense)