Question

two stones are falling at a place from the Heights in the ratio of 2 :3 find their velocities on reaching the ground are in the ratio

Answer 1

4:9 ll be their velocity ratio

Answer 2

The stones are under free fall. Hence, the acceleration of the stone will be the acceleration due to gravity.

The two stones are falling from different heights.

Let the heights are denoted as  $h_{1} \ and\ h_{2}\ respectively$

As per the question ,  $h_{1} :h_{2}=2:3$

Let the velocities of each ball after reaching earth is denoted as-

                                                          $v_{1}\ and\ v_{2} \ respectively$

From equation of kinematics we know that-

                                            $v^2-u^2=2as$

Here v is the final velocity and u is the initial velocity.

s is the distance travelled and a is the acceleration.

For motion under free fall a=g

                                           u=0

                                           s=h

                              Hence,  $v^2-0=2gh$

                                             $v^2\ \alpha\ h$

                                             $\frac{v_{1}^2} { v_{2}^2} =\frac{h_{1}} {h_{2}}$  

                                                $=\ \frac{2}{3}$

                                               $\frac{v_{1}} {v_{2}}=\sqrt{ \frac{2}{3}}$

       $Hence\ v_{1}: v_{2} =\sqrt{2}: \sqrt{3}$   [ans]