The acceleration due to gravity on planet X is

one fifth that on the surface of the earth.
If it takes 3.5 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?
Answer in units of s.

Well, on planet X, gravity is one-fifth that of Earth's gravity. So, it would take five times longer for the object to fall the same distance. Therefore, on planet X, it would take 3.5 s * 5 = 17.5 seconds. That sounds like a slow descent, which gives you plenty of time to enjoy the view... or take a nap on the way down!

The acceleration due to gravity on planet X is one-fifth that on the surface of the earth. Let's denote the acceleration due to gravity on earth as g and on planet X as gX.

We know that gX = (1/5)g.

The time it takes for an object to fall a certain distance from rest can be calculated using the formula:

t = sqrt(2d/g), where t is the time, d is the distance, and g is the acceleration due to gravity.

On earth, we have t = 3.5 s and g = g (acceleration due to gravity on earth).

On planet X, we need to find the time tX when g = gX.

Using the formula, we have:

tX = sqrt(2d/gX).

Substituting gX = (1/5)g, we get:

tX = sqrt(2d/(1/5)g).

Simplifying the expression, we can rewrite it as:

tX = sqrt(10d/g).

Now, since the distance (d) is the same on both earth and planet X, we can substitute the expression for t from the earth into the planet X equation:

tX = sqrt(10d/g) = sqrt(10*(3.5)/(1/5)) = sqrt(10*3.5*5) = sqrt(175) = 13.23 s.

Therefore, it would take approximately 13.23 seconds for the object to fall the same distance on planet X.

To find the time it would take for an object to fall the same distance on planet X, we can use the equation for free fall:

d = 0.5 * g * t^2

where:
d = distance
g = acceleration due to gravity
t = time

Let's start by finding the acceleration due to gravity on planet X. Given that it is one fifth that on the surface of the earth, we can write:

gX = (1/5) * g (where g is the acceleration due to gravity on earth)

Next, we can rearrange the equation for free fall to solve for time:

t = √(2 * d / g)

On earth, the time is given as 3.5 seconds, and we want to find the time on planet X. Let's substitute the known values into the equation:

3.5 = √(2 * d / g)

Now, we can solve for tX by rearranging the equation:

tX = √(2 * d / gX)

Substituting the value of gX, we get:

tX = √(2 * d / ((1/5) * g))

Simplifying further:

tX = √(10 * (2 * d / g))

Therefore, the time it would take for an object to fall the same distance on planet X is the square root of 10 times the time it takes on Earth.

The time to fall a given distance is inversely proportional to the square root of g. That time is 2.24 times longer if the time is 5 times less.

What is 2.24 x 3.5 s ?