STD 11 - 3.2. motion in plane — NEET STD 11 Science — Question

$R=\frac{u^{2} \sin 2 \theta}{g}$

The time of flight of projectile motion is given as,

$T=\frac{2 u \sin \theta}{g}$

The square of time of flight of projectile motion is,

$T^{2}=\left(\frac{2 u \sin \theta}{g}\right)^{2}$

$=\frac{4 u^{2} \sin ^{2} \theta}{g^{2}}$

The ratio of maximum range and square of time of flight in projectile motion is calculated as,

$\frac{R}{T^{2}}=\frac{\frac{u^{2} \sin 2 \theta}{g}}{\frac{4 u^{2} \sin ^{2} \theta}{g^{2}}}$

$=\frac{g}{2} \cot \theta$