question_answer

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights,\[{{h}_{1}}\]and \[{{h}_{2}}.\]Which of the following is correct? [JEE Main 12-4-2019 Afternoon]

A) (a)\[{{R}^{2}}=2\,{{h}_{1}}{{h}_{2}}\]

B) (b)\[{{R}^{2}}=16\,{{h}_{1}}{{h}_{2}}\]

C) (c)\[{{R}^{2}}=4\,{{h}_{1}}{{h}_{2}}\]

D) (d)\[{{R}^{2}}=\,{{h}_{1}}{{h}_{2}}\]

Correct Answer: B

Solution :

[b]

For same range angle of projection will be\[\theta \And 90-\theta \]

\[R=\frac{{{u}^{2}}2\sin \theta \cos \theta }{g}\]

\[{{h}_{1}}=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{g}\]

\[{{h}_{2}}=\frac{{{u}^{2}}{{\sin }^{2}}(90-\theta )}{g}\]

\[\frac{{{R}^{2}}}{{{h}_{1}}{{h}_{2}}}=16\]