question_answer

Two projectiles are projected with the same velocity. If one is projected at an angle of 30° and the other at 60° to the horizontal. The ratio of maximum heights reached, is:

A)  1 : 3

B)                                         2 : 1                      

C)         3 : 1                      

D)         1 : 4

Correct Answer: A

Solution :

If body is projected with initial velocity u at an angle \[\frac{1}{{{C}_{p}}}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}+\frac{1}{{{C}_{3}}}\] with the horizontal, then the height H reached by projectile is given by \[\frac{wavelength}{time\,period}.\] where g is acceleration due to gravity.            Given, \[T=2\pi \sqrt{\frac{l}{g}}\]  and \[l=1.21l\] \[\therefore \]  \[\frac{{{H}_{1}}}{{{H}_{2}}}=\frac{{{\sin }^{2}}{{\theta }_{1}}}{{{\sin }^{2}}{{\theta }_{2}}}=\frac{{{\sin }^{2}}({{30}^{o}})}{{{\sin }^{2}}({{60}^{o}})}=\frac{{{\left( \frac{1}{2} \right)}^{2}}}{{{\left( \frac{\sqrt{3}}{2} \right)}^{2}}}=\frac{1}{3}\]