A) \[{{\tan }^{-1}}\frac{1}{5}\]
B) \[{{\tan }^{+1}}\frac{1}{5}\]
C) \[{{\tan }^{-1}}1\]
D) \[{{\tan }^{-1}}5\]
Correct Answer: A
Solution :
Here: Speed of bomber plane \[v=500\,\,m/s\] Time taken by bomb to strike the ground \[t=10\sec \] and \[g=10\,\,m/{{s}^{2}}\] Using the relation \[t=\sqrt{\frac{2h}{g}}\] or \[\frac{2h}{10}={{10}^{2}}\] or \[2h=1000\], So, \[h=500\,\,m\] The vertical velocity \[=\sqrt{2gh}=\sqrt{2\times 10\times 500}=100\,\,m/s\] Hence, \[\tan \theta =\frac{vertical\,\,velocity}{horizontal\,\,velocity}=\frac{100}{500}=\frac{1}{5}\] or \[\theta ={{\tan }^{-1}}\frac{1}{5}\]
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