Kinematics Question 614
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} ) $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] max heigth, ${{H_A}}=\frac{u_{A^2}{{\sin }^{2}}30{}^\circ }{2{g}}; $
$ {{H} _{B}}= \frac{u_B^{2}{{\sin }^{2}}\theta } {2g} $
As we know , ${{{H}} _{{A}}}{=}{{{H}} _{{B}}} $
$ \frac{u_{A^2}{{\sin }^{2}}30{}^\circ }{2{g}}=\frac{{u_B^{2}}{{\sin }^{2}}\theta }{2{g}} $
$ \Rightarrow \frac{{\sin^{2}}}\theta {{\sin^{2}}30{}^\circ }=\frac{{u_A^{2}}}{{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} ) $
