A ball is projected at an angle of $30°$ above with the horizontal from the top of a tower and strikes the ground in $5 \mathrm{s}$ at an angle of $45°$ with the horizontal. Find the speed with which it was projected.

• Correct answer
  A

  $50\left(\sqrt{3}-1\right) {\text{m s}}^{-1}$
• B

  $50\left(\sqrt{2}-1\right) {\text{m s}}^{-1}$
• C

  $70\left(\sqrt{3}-1\right) {\text{m s}}^{-1}$
• D

  $80\left(\sqrt{3}-1\right) {\text{m s}}^{-1}$

Solution

$v_{\mathrm{x}} = - v_{\mathrm{y}}$



$u \cos 30° = - (u \sin 30° - gt)$

$u\frac{\sqrt{3}}{2}=-\left(\frac{u}{2}-10\times 5\right)$

$u\left(\frac{\sqrt{3}+1}{2}\right)=50$

$\Rightarrow u=100\left(\frac{1}{\sqrt{3}+1}\right)\Rightarrow u=50\left(\sqrt{3}-1\right) {\text{m s}}^{-1}$
 

Hence, the correct answer is option: 'A'.