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

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

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

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

Correct Answer: B

Solution :

For same range angle of projection will be\[\theta \And 90-\theta \] \[R=\frac{{{u}^{2}}2\sin \theta \cos \theta }{g}\] \[{{h}_{1}}=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{g}\] \[{{h}_{2}}=\frac{{{u}^{2}}{{\sin }^{2}}(90-\theta )}{g}\] \[\frac{{{R}^{2}}}{{{h}_{1}}{{h}_{2}}}=16\]