A) \[\frac{{{h}_{1}}t_{2}^{2}-{{h}_{2}}t_{1}^{2}}{{{h}_{1}}{{t}_{2}}-{{h}_{2}}{{t}_{1}}}\]
B) \[\frac{{{h}_{1}}t_{2}^{2}+{{h}_{2}}t_{1}^{2}}{{{h}_{1}}{{t}_{2}}+{{h}_{2}}{{t}_{1}}}\]
C) \[\frac{{{h}_{1}}{{t}_{2}}}{{{h}_{1}}{{t}_{2}}-{{h}_{2}}{{t}_{1}}}\]
D) None
Correct Answer: A
Solution :
| [a] \[{{\text{h}}_{\text{1}}}\text{=}\,\,\text{u sin}\,\theta \,{{\text{t}}_{\text{1}}}\text{+}\frac{\text{1}}{\text{2}}\text{gt}_{\text{1}}^{\text{2}}\text{ };\] |
| \[{{\text{h}}_{2}}\,\text{=}\,\,\text{u sin}\,\theta \,{{\text{t}}_{2}}\text{+}\frac{\text{1}}{\text{2}}\text{gt}_{2}^{\text{2}}\] |
| \[\text{So, }\frac{{{\text{t}}_{\text{1}}}}{{{\text{t}}_{2}}}=\frac{{{h}_{1}}+\frac{\text{1}}{\text{2}}\text{gt}_{\text{1}}^{\text{2}}}{{{\text{h}}_{2}}+\frac{\text{1}}{\text{2}}\text{gt}_{2}^{\text{2}}}\] |
| \[\Rightarrow {{h}_{1}}{{t}_{2}}-{{h}_{2}}{{t}_{1}}=\frac{1}{2}g\left( {{t}_{1}}t_{2}^{2}-t_{1}^{2}t_{2}^{{}} \right)\] |
| Time of flight \[\text{= 2u sin}\theta /\text{g=}\frac{{{h}_{1}}t_{2}^{2}-{{h}_{2}}t_{1}^{2}}{{{h}_{1}}{{t}_{2}}-{{h}_{2}}{{t}_{1}}}\] |
| [Use above eqn. to simplify] |
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