Question

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

• A. $50(\sqrt{3}-1)\mathrm{m}{\mathrm{s}}^{-1}$
• B. $50(\sqrt{2}-1)\mathrm{m}{\mathrm{s}}^{-1}$
• C. $70\left(\sqrt{3}-1\right){\left(\text{m s}\right)}^{-1}$
• D. $80\left(\sqrt{3}-1\right){\left(\text{m s}\right)}^{-1}$

Answer 1

Answer: (A)

$v_x=-v_y$

$ucos30^{\circ }=-(usin30^{\circ }-gt)$
$u\frac{\sqrt{3}}{2}=-\left(\frac{u}{2}-10\times 5\right)$
$u\left(\frac{\sqrt{3}+1}{2}\right)=50$
$\Rightarrow u=100\left(\frac{1}{\sqrt{3}+1}\right)\Rightarrow u=50\left(\sqrt{3}-1\right){\left(\text{m s}\right)}^{-1}$