Question

An object is dropped from the height h. The velocity with which it hits the ground is (a) √(2gh) (b) √(2g/h) (c) √(2h/g) (d) √(gh/2​

Answer 1

Given,

An object is dropped from the height 'h'.

To find,

The velocity with which it hits the ground.

Solution,

We can simply solve this numerical problem by using the following process.

Here,

It is assumed that the object starts from rest.

So,

Initial velocity (u) = 0

Final velocity (v) = ?

Acceleration (a) = g [As the object falls from a height, so the acceleration caused here will be the aceleration due to gravity.]

Displacement (s) = h [The height from where the object is dropped.]

Now, applying the kinematics formula, we get,

v² = u²+2as

v² = (0)²+(2×g×h)

v² = 2gh

v = √(2gh)

[This will be considered as the final result.]

Hence, the final velocity will be √(2gh)

Answer 2

Here it is given that an object is dropped from a height h.

We have to find the velocity with which it hits the ground

Now, as the object is dropped, the initial velocity will be 0

So, u = 0

The displacement will be h

And acceleration will be the acceleration due to gravity

We will use the 3rd kinematical equation

$v^{2} =u^{2} +2as$

Putting the values

$v^{2} = 0 + 2gh\\v=\sqrt{2gh}$

So, option a will be the correct answer.