The acceleration due to gravity on planet X is

one fifth that on the surface of the earth.
If it takes 3.9 s for an object to fall a certain
distance from rest on earth, how long would
it take to fall the same distance on planet X?

112

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To determine how long it would take for an object to fall the same distance on planet X, we need to consider the difference in acceleration due to gravity between planet X and the Earth.

Acceleration due to gravity on Earth (gEarth) is approximately 9.8 m/s².

Given that the acceleration due to gravity on planet X is one fifth that on the surface of the Earth, we can calculate the acceleration due to gravity on planet X (gX) as follows:

gX = (1/5) * gEarth
= (1/5) * 9.8 m/s²
= 1.96 m/s²

Now, using the equation for the distance fallen by an object in free fall:

d = (1/2) * g * t²

where d is the distance, g is the acceleration due to gravity, and t is the time taken, we can solve for the time taken on planet X.

Given that the distance (d) and acceleration due to gravity (gX) on planet X are equivalent to the values on Earth, we can rearrange the equation to solve for t:

t = √(2 * d / gX)

Substituting the values, we have:

t = √(2 * d / 1.96)

To find the time it takes to fall the same distance on planet X, we need the value of d (the specific distance). Once we have that value, we can substitute it into the equation to find the time taken.