question_answer

A particle of mass m is projected from a fixed point 0 into the air with velocity u in a direction making an angle a with the horizontal. Then the motion of the particle describes a parabola with the latusrectum is

A)  \[\frac{2}{g}{{(horizontal\text{ }velocity)}^{2}}\]

B)  \[\frac{2}{g}(vertical\text{ }velocity)\]

C)  \[\frac{2}{{{g}^{2}}}{{(horizontal\text{ }velocity)}^{2}}\]

D)  \[\frac{2}{{{g}^{2}}}{{(vertical\text{ }velocity)}^{2}}\]

Correct Answer: A

Solution :

We know, Latusrectum \[=\frac{2{{u}^{2}}}{g}\,{{\cos }^{2}}\alpha \] \[=\frac{2}{g}\] \[{{(horizontal\text{ }velocity)}^{2}}\]