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 $5 \, s$ 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)

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

$u \, cos \, 30^\circ \, = \, - \, \left(\right.u \, sin \, 30^\circ \, - \, gt\left.\right)$
$u\frac{\sqrt{3}}{2}=-\left(\frac{u}{2} - 1 0 \times 5\right)$
$u\left(\frac{\sqrt{3} + 1}{2}\right)=50$
$\Rightarrow u=100\left(\frac{1}{\sqrt{3} + 1}\right)\Rightarrow \, u=50\left(\sqrt{3} - 1\right) \, \left(\text{m s}\right)^{- 1}$