Physics Two Dimensional Motion Question 162
Question: Two pegs A and B thrown with speeds in the ratio 1:3 acquired the same heights. If A is thrown at an angle of $ 30{}^\circ $ with the horizontal, the angle of projection of B will be
Options:
A) $ 0{}^\circ $ B)$ si{{n}^{-1}}( \frac{1}{8} ) $ C) $ si{{n}^{-1}}( \frac{1}{6} ) $ D)$ si{{n}^{-1}}( \frac{1}{2} ) $
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Answer:
Correct Answer: C
Solution:
[c] $ \text{max heigth, }{{\text{H}} _{\text{A}}}=\frac{\text{u} _{A^{2}{{\sin }^{2}}30{}^\circ }{2\text{g}}; $ $ {{\text{H}} _{\text{B}}}=\frac{\text{u} _{B^{2}{{\sin }^{2}}\theta }{2\text{g}} $ $ \text{As we know, }{{\text{H}} _{\text{A}}}\text{=},,{{\text{H}} _{\text{B}}} $ $ \frac{\text{u} _{A^{2}{{\sin }^{2}}30{}^\circ }{2\text{g}}=\frac{\text{u} _{B^{2}{{\sin }^{2}}\theta }{2\text{g}} $ $ \Rightarrow \frac{{{\sin }^{2}}\theta }{{{\sin }^{2}}30{}^\circ }=\frac{\text{u} _{A^{2}}{\text{u} _{B^{2}} $ $ {{\sin }^{2}}\theta ={{( \frac{u _{A}}{u _{B}} )}^{2}}{{\sin }^{2}}30{}^\circ \Rightarrow {{\sin }^{2}}\theta =\frac{1}{36} $ $ \sin \theta =\frac{1}{6}\Rightarrow \theta ={{\sin }^{-1}}( \frac{1}{6} ) $
BETA
