A) \[{{\tan }^{-1}}\left( \frac{1}{5} \right)\]
B) \[\tan \left( \frac{1}{5} \right)\]
C) \[{{\tan }^{-1}}(1)\]
D) \[{{\tan }^{-1}}(5)\]
Correct Answer: A
Solution :
Time taken by the bomb to strike ground is given by \[t=\sqrt{\frac{2h}{g}}\] \[10=\sqrt{\frac{2h}{10}}\]or \[100=\frac{2h}{10}\] or \[2h=1000\] \[\Rightarrow \] \[h=500\,m\] Vertical velocity is \[\upsilon =\sqrt{2g\,h}=\sqrt{2\times 10\times 500}=100\,m/s\] Hence, \[\text{tan}\,=\frac{\text{vertical}\,\text{velocity}}{\text{horizontal}\,\text{velcity}}\] \[\tan \theta =\frac{100}{500}=\frac{1}{5}\] \[\theta ={{\tan }^{-1}}\left( \frac{1}{5} \right)\]
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