Question

A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is:

Answer 1

given

horizontal range$=u^2\sin \frac{2Ф}{g}$

maximum height$=u^2{\sin }^2\frac{Ф}{2g}$

horizontal range = 3$\times$ maximum height

$u^2\sin \frac{2Ф}{g}=3\times u^2{\sin }^2\frac{Ф}{2g}$

$\sin 2Ф=2\sin Ф.\cos Ф$

$2\sin Ф.\cos Ф=\frac{3}{2}.{\sin }^2Ф$

$\tan Ф=\frac{4}{3}$

$Ф=\tan ⁻¹\left(\frac{4}{3}\right)$