if the final velocities of two bodies falling freely is 4:3 then ratio of heights from which they fall is

Dear Student,

Please find below the solution to the asked query:

Suppose their height are h₁ and h₂ respectively. So the final velocities will be 
$v_1=\sqrt{2g{h}_1}$
and
$v_2=\sqrt{2g{h}_2}$
so we have
$$\begin{gathered} \frac{v_1}{v_2}=\frac{\sqrt{2g{h}_1}}{\sqrt{2g{h}_2}}=\frac{\sqrt{h_1}}{\sqrt{h_2}} \\ \Rightarrow \frac{h_1}{h_2}={\left(\frac{v_1}{v_2}\right)}^2=\frac{16}{9} \end{gathered}$$
so the ratio between heights will be 16:9. 

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