Question

If ratio of time of fall of two bodies 1 : 2, what is the ratio of their

height of fall?​

Answer 1

$\displaystyle t = \sqrt{\dfrac{2g}{h}}\implies t\;\alpha \;\dfrac{1}{\sqrt{h}}\\\\\displaystyle \dfrac{t_1}{t_2} =\sqrt{\dfrac{h_2}{h_1}}\implies\dfrac{h_1}{h_2} =\left(\dfrac{t_2}{t_1}\right)^2 =\left(\dfrac{2}{1}\right)^2=4$

Answer 2

Answer:

$\frac{f^1}{f^2} = \frac{3}{4}$

Explanation:

Solution :

$s = ut + \frac{1}{2} gt.^{2}$ when $u = 0 , s=\frac{1}{2} gt.^{2}$ i.e,. $s$ ∝ $t^{2}$

$\frac{h^{1} }{h^{2} } =(\frac{t^{1} }{t^{2} } ) ^{1}$ $= (\frac{1}{2} )^{2}$ $= \frac{1}{4}$

( b ) $\frac{h^{1}}{h^{2}} = \frac{t^1}{t^2_{2} } = \frac{9}{4}$ ∴ $\frac{f^1}{f^2} = \frac{3}{4}$

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