Question

The time taken by an object dropped on vacuum to reach the ground depends on acceleration due to gravity g and height h. Derive the relationship between t, g and h.

Answer 1

Given:

The time taken by an object dropped (in vacuum) to reach the ground depends on acceleration due to gravity g and height h.

To find:

Relationships between g, h and t

Calculation:

Considering gravitational acceleration to be a constant value irrespective of the height of the object from the Earth surface , we can apply the equations of kinematics to solve this problem.

Since the object has been dropped from the given height, we can say that its initial velocity (u) is zero.

Applying 2nd Equation of Kinematics:

$\therefore \: s = ut + \dfrac{1}{2} a {t}^{2}$

$= > \: h = (0 \times t) + \dfrac{1}{2} g {t}^{2}$

$= > \: h = \dfrac{1}{2} g {t}^{2}$

So the required relation is :

$\boxed{ \sf{\: h = \dfrac{1}{2} g {t}^{2} }}$