Question

a ball is dropped from height h its velocity when its reaches ground (A)independent of h B. Directly proportional to h C. Proportional to square root of h D.none of these

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

⟶ A ball is dropped from height h.

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

➝ Relation b/w final velocity (v) at which ball touched the ground and height (h).

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

➠ Here, Acceleration due to gravity continuously acts in downward direction.

➠ We know that, Acceleration due to gravity has constant magnitude so, we can apply equation of kinematics to solve this question.

Let's apply 3rd eq. of kinematics

$:\implies\tt\:v^2-u^2=2gh$

$:\implies\tt\:v^2-0^2=2gh$

$:\implies\tt\:v^2=2gh$

$:\implies\tt\:v=\sqrt{2gh}$

$:\implies\underline{\boxed{\bf{\purple{v\propto\sqrt{h}}}}}$

Option-C is the correct answer.