Question

A body is dropped from a height of h and it
falls under an acceleration due to gravity g.
Find the time it will require to reach the
ground in terms of h and g.​

Answer 1

Given :-

→ Height from which, the body

is dropped = h

→ Acceleration due to gravity = g

To find:-

→ Time taken by the body to reach the

ground in terms of h and g.

Solution:-

Let the time required time be 't'.

As the body is freely falling, so in this case :-

• Initial velocity [u] of the body will be

equal to zero.

• Acceleration due to gravity [g], will be

taken as positive.

By using the 2nd equation of motion,

we get :-

=> h = ut + 1/2gt²

=> h = 0(t) + 1/2gt²

=> h = 1/2gt²

=> 2h = gt²

=> t² = 2h/g

=> t = √2h/g

Thus, time required by the body to reach the ground in terms of 'h' and 'g' is √2h/g .

Some Extra Information:-

The three equations of motion for a freely falling body are :-

• v = u +gt

• h = ut + 1/2gt²

• v² - u² = 2gh

Answer 2

We have,

Height = h

Acceleration due to gravity = g

Initial velocity = u = 0

We know,

h = ut + ½gt²

⇒h = ½gt²

⇒t² = 2h/g

⇒t = √2h/g {Answer}