# The acceleration due to gravity on planet X is one fifth of that on the surface of the Earth. If it takes 3.4 s for an object to fall a certain distance from rest on Earth, how long would it take...

The acceleration due to gravity on planet X is one fifth of that on the surface of the Earth. If it takes 3.4 s for an object to fall a certain distance from rest on Earth, how long would it take for the object to fall the same distance on planet X? Answer in the units of s.

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The equation of the fall from rest under the influence of only gravity is

`x = g*t^2/2` , where *x *is the height of the fall, *a* is the acceleration due to gravity, and *t *is the time during which the fall took place.

For the object on the surface of the Earth, acceleration due to gravity is g = 9.8 m/s^2 and the time `t_E` of the fall from rest is 3.4 s.

For the object on planet X, the acceleration due to gravity is g/5. Then, the time `t_x` of the fall from rest from the same height can be determined from

`g (3.4)^2/2 = 1/2*g/5*t_x^2`

From here,

`t_x = sqrt(5)*3.4 s=7.6 s` .

It would take `sqrt(5)`

times longer for the object to fall on the planet where the gravity is five times weaker.

**On planet X, it would take the object 7.6 seconds to fall the same distance.**