A) \[\theta \]
B) \[{{\tan }^{-1}}\left( \theta /\text{t} \right)\]
C) \[{{\tan }^{-1}}\left( \frac{\text{v cos}\theta }{\text{v sin}\theta -\text{gt}} \right)\]
D) \[{{\tan }^{-1}}\left( \frac{\text{v sin}\theta -\text{gt}}{\text{v cos}\theta } \right)\]
Correct Answer: D
Solution :
| [d] Horizontally after time |
| \[v\,\,\cos \theta =v\,\,\cos \beta \] ?(i) |
| [\[\beta \]= angle with horizontal after time t] |
| Vertically, \[v\,\,\sin \theta -gt=v\,\,\sin \,\beta \] ?(ii) |
| Dividing on (ii)/ (i) we get \[\tan \beta =\frac{v\sin \theta -\text{gt}}{v\cos \theta }\]\[\tan \beta =\frac{v\sin \theta -\text{gt}}{v\cos \theta }\Rightarrow \beta ={{\tan }^{-1}}\left( \frac{v\sin \theta -gt}{v\cos \theta } \right)\] |
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