Two stones are projected from the top of a cliff $\mathrm{h}$ metres high, with the same speed $\mathrm{u}$,…

Two stones are projected from the top of a cliff $\mathrm{h}$ metres high, with the same speed $\mathrm{u}$, so as to hit the ground at the same spot. If one of the stones is projected at an angle $\theta$ to the horizontal then the $\theta$ equals
  1. $\mathrm{u} \sqrt{\frac{2}{\mathrm{gh}}}$
  2. $\sqrt{\frac{2 \mathrm{u}}{\mathrm{gh}}}$
  3. $2 \mathrm{~g} \sqrt{\frac{\mathrm{u}}{\mathrm{h}}}$
  4. $2 \mathrm{~h} \sqrt{\frac{\mathrm{u}}{\mathrm{g}}}$

Solution

$\mathrm{R}=\mathrm{u} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}=(\mathrm{u} \cos \theta) \times \mathrm{t}$ $t=\frac{1}{\cos \theta} \sqrt{\frac{2 h}{g}}$

Asked in: JEE Main 2003

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