A) (a)\[{{\tan }^{-1}}\frac{2}{3}\]
B) (b)\[{{\tan }^{-1}}\frac{3}{2}\]
C) (c)\[{{\tan }^{-1}}\frac{7}{4}\]
D) (d)\[{{\tan }^{-1}}\frac{4}{5}\]
Correct Answer: C
Solution :
| [c] From question, Horizontal velocity (initial), |
| \[{{u}_{x}}=\frac{40}{2}=20m/s\] |
| Vertical velocity (initial), \[50={{u}_{y}}t+\frac{1}{2}g{{t}^{2}}\] |
| \[\Rightarrow \]\[{{u}_{y}}\times 2+\frac{1}{2}(-10)\times 4\]or\[50=2{{u}_{y}}-20\] |
| or\[{{u}_{y}}=\frac{70}{2}=35m/s\] |
| \[\therefore \]\[\tan \theta =\frac{{{u}_{y}}}{{{u}_{x}}}=\frac{35}{20}=\frac{7}{4}\]\[\Rightarrow \] |
| Angle\[\theta ={{\tan }^{-1}}\frac{7}{4}\] |
| \[\therefore \]\[\frac{\sin {{\theta }_{c}}}{\sin {{\theta }_{s}}}=\frac{\frac{5}{7}g}{\frac{2}{3}g}=\frac{15}{14}\] |
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