A) \[{{\sin }^{-1}}\frac{1}{5}\]
B) \[ta{{n}^{-1}}\frac{1}{5}\]
C) \[ta{{n}^{-1}}\,5\]
D) \[ta{{n}^{-1}}\,1\]
Correct Answer: B
Solution :
Here: Speed of the bomber plane \[V=\text{ }500\text{ }m/s\]. Time taken by the bomb to strike the ground \[=10\sec .\] \[g=10\,m/{{s}^{2}}\] \[\therefore \] Time is given by \[t=\sqrt{\frac{2h}{g}}\] \[\Rightarrow \] \[10=\sqrt{\frac{2h}{g}}\] \[\Rightarrow \] \[\frac{2h}{g}={{(10)}^{2}}=100\] \[\Rightarrow \] \[2h=100\times 10\] \[\Rightarrow \] \[h=500\,m.\] and vertical velocity is given by \[V=\sqrt{2gh}\] \[V=\sqrt{2\times 10\times 500}=100\,m/s.\] Therefore, \[\tan \theta =\frac{vertical\text{ }velocity}{horizontal\text{ }velocity}\] \[=\frac{100}{500}=\frac{1}{5}\] \[\theta ={{\tan }^{-1}}\left( \frac{1}{5} \right)\]
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