A) \[{{t}_{1}}{{t}_{2}}\propto \,{{R}^{2}}\]
B) \[{{t}_{1}}{{t}_{2}}\propto \,R\]
C) \[{{t}_{1}}{{t}_{2}}\propto \,\frac{1}{R}\]
D) \[{{t}_{1}}{{t}_{2}}\propto \,\frac{1}{{{R}^{2}}}\]
Correct Answer: B
Solution :
For same range angle of projection should be q and 90?q So, time of flights \[{{t}_{1}}=\frac{2u\sin \theta }{g}\] and \[{{t}_{2}}=\frac{2u\sin (90-\theta )}{g}=\frac{2u\cos \theta }{g}\] By multiplying\[={{t}_{1}}{{t}_{2}}=\frac{4{{u}^{2}}\sin \theta \cos \theta }{{{g}^{2}}}\] \[{{t}_{1}}{{t}_{2}}=\frac{2}{g}\frac{({{u}^{2}}\sin 2\theta )}{g}=\frac{2R}{g}\] Þ \[{{t}_{1}}{{t}_{2}}\propto R\]
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