First slide

The 3 equation for uniform acc

Question

A stone is allowed to fall freely from rest. The ratio of the time taken to fall through the first metre and the second metre distance is

Moderate

A

$\sqrt{2} - 1$
B

$\sqrt{2} + 1$
C

$\sqrt{2}$
D

None of these

Solution

$1 = \frac{1}{2} g t_{1}^{2} or t_{1} = \sqrt{\frac{2}{g}}$
$2 = \frac{1}{2} g t^{2} or t = \sqrt{\frac{4}{g}}$
But $t_{2} = t - t_{1} = \sqrt{\frac{4}{g}} - \sqrt{\frac{2}{g}}$
$∴$ $\frac{t_{1}}{t_{2}} = \frac{\sqrt{2 / g}}{\sqrt{4 / g} - \sqrt{2 / g}} = \frac{\sqrt{2}}{2 - \sqrt{2}}$
$= \frac{\sqrt{2} (2 + \sqrt{2)}}{2} = (\sqrt{2} + 1)$

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