A) \[{{t}_{1}}{{t}_{2}}\propto R\]
B) \[{{t}_{1}}{{t}_{2}}\propto {{R}^{2}}\]
C) \[{{t}_{1}}{{t}_{2}}\propto \frac{1}{{{R}^{2}}}\]
D) \[{{t}_{1}}{{t}_{2}}\propto \frac{1}{R}\]
Correct Answer: A
Solution :
Time of flight of a projectile is given as,\[T=\frac{2u\sin \theta }{g}\] Hence, \[{{t}_{1}}=\frac{2u\,\sin \theta }{g}\] and \[{{t}_{2}}=\frac{2u\,\sin (90-\alpha )}{g}\] So, \[{{t}_{1}}\times {{t}_{2}}\,=2\frac{{{u}^{2}}}{{{g}^{2}}}\sin 2\alpha \] As, range of projectile is given as \[R=\frac{{{u}^{2}}\,\sin 2\alpha }{g}\] Hence, \[{{t}_{1}}\times {{t}_{2}}\,\frac{2R}{g}\,\Rightarrow \,{{t}_{1}}\,\times {{t}_{2}}\propto R\]
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