question_answer

A body of mass m is thrown with velocity u at an angle \[\text{3}0{}^\circ \] to the horizontal and another body B of the same mass is thrown with velocity u at an angle of \[\text{6}0{}^\circ \] to the horizontal, find the ratio of the horizontal range and max. height of A and B.

Answer:

                Case (i) When \[\theta ={{30}^{\text{o}}}\]; \[{{R}_{A}}=\frac{{{u}^{2}}}{g}\sin 2\times {{30}^{\text{o}}}=\frac{{{u}^{2}}}{g}\times \frac{\sqrt{3}}{2}\];  \[{{H}_{A}}=\frac{{{u}^{2}}}{2g}{{\sin }^{2}}{{30}^{\text{o}}}=\frac{{{u}^{2}}}{2g}\times \frac{1}{4}\] Case (ii) When\[\theta =\text{6}0{}^\circ \];  \[{{R}_{B}}=\frac{{{u}^{2}}}{g}\sin 2\times {{60}^{\text{o}}}=\frac{{{u}^{2}}}{2}\times \frac{\sqrt{3}}{2}\]; \[{{H}_{B}}=\frac{{{u}^{2}}}{2g}{{\sin }^{2}}{{60}^{\text{o}}}=\frac{{{u}^{2}}}{2g}\times \frac{3}{4}\] \[\therefore \]  \[{{R}_{A}}:{{R}_{B}}=1:1\]and\[{{H}_{A}}:{{H}_{B}}=1:3\]