Ratio between maximum range and square of tim | vedclass

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Question

The maximum range of projectile motion is given as,

$R=\frac{u^{2} \sin 2 	heta}{g}$

The time of flight of projectile motion is given as,

$T

Vedclass · Accepted Answer

$\frac{g}{2}$

Vedclass · Answer

The maximum range of projectile motion is given as,

$R=\frac{u^{2} \sin 2 	heta}{g}$

The time of flight of projectile motion is given as,

$T=\frac{2 u \sin 	heta}{g}$

The square of time of flight of projectile motion is,

$T^{2}=\left(\frac{2 u \sin 	heta}{g}ight)^{2}$

$=\frac{4 u^{2} \sin ^{2} 	heta}{g^{2}}$

The ratio of maximum range and square of time of flight in projectile motion is calculated as,

$\frac{R}{T^{2}}=\frac{\frac{u^{2} \sin 2 	heta}{g}}{\frac{4 u^{2} \sin ^{2} 	heta}{g^{2}}}$

$=\frac{g}{2} \cot 	heta$

Ratio between maximum range and square of time of flight in projectile motion is

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