#### Given below are two statements:One is labelled as Assertion A and the other is labelled as Reason RAssertion A: Two identical balls A and B thrown with same velocity $\mathrm{'u'}$ at two different angles with horizontal attained the same $\mathrm{h_{1}}$range R. If A and B reached the maximum height $\mathrm{h_{1}}$ and $\mathrm{h_{2}}$ respectively,then $\mathrm{R=4\sqrt{h_{1}h_{2}}}$Reason R: Product of said heights.$\mathrm{h_{1}h_{2}=\left ( \frac{u^{2}\sin^{2}\theta}{2g} \right ).\left ( \frac{u^{2}\cos^{2} \theta}{2g} \right )}$Question: Choose the correct answer:Option: 1 Both A and R are true and R is the correct explanation of A.Option: 2 Both A and R are true but R is the NOT the correct explanation of A.Option: 3 A is true but R is false.Option: 4 A is false but R is true.

For two balls $\mathrm{A\: and \: B}$ thrown with the same velocity $\mathrm{'u'}$ at two different angles with horizontal obtained the same range $\mathrm{R}$ then their angles of projection let say $\mathrm{\alpha \: and \: \beta }$ respectively will have a relation

$\mathrm{\alpha+\beta=90^{\circ}}\\$

If  $\mathrm{ \alpha=\theta, }$ then $\mathrm{ \beta=90- \alpha=90 - \theta }$

$\mathrm{h_{1}=\frac{u^{2} \sin \theta}{2 g} ; h_{2}=\frac{u^{2} \sin (90-\theta)}{2 g}}\\$

$\mathrm{h_{2}=\frac{u^{2} \cos \theta}{2 g}}\\$

$\mathrm{R=\frac{2 u \sin \theta \cos \theta}{g}=4 \sqrt{h_{1} h_{2}}}$

Hence the correct answer is option 1.