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