Two projectiles thrown at 30° and 45° with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :

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$1 : \sqrt{2}$

2 : 1

1 : 2

$\sqrt{2} : 1$

answer is C.

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Detailed Solution

$\begin{array}{l} ∵ t_{a} = \frac{usin θ}{g} \\ \Rightarrow \frac{u_{1} \sin (30^{\circ})}{g} = \frac{u_{2} \sin (45^{\circ})}{g} \\ \Rightarrow \frac{u_{1}}{u_{2}} = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} = \frac{\sqrt{2}}{1} \end{array}$

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