The equation of motion of a projectile is:&nb | vedclass

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Question

$y=12 x-\frac{3}{4} x^{2}$

$\frac{d y}{d t}=12 \frac{d x}{d t}-\frac{3}{2} x \frac{d x}{d t}$

At $x=0: \quad \frac{d y}{d t}=12 \frac{d x}{d t}$

Vedclass · Accepted Answer

$21.6$

Vedclass · Answer

$y=12 x-\frac{3}{4} x^{2}$

$\frac{d y}{d t}=12 \frac{d x}{d t}-\frac{3}{2} x \frac{d x}{d t}$

At $x=0: \quad \frac{d y}{d t}=12 \frac{d x}{d t}$

If $	heta$ be the angle of projection, then

$\frac{d y / d t}{d x / d t}=12=	an 	heta$

Also, if $u$ $=$initial velocity, then $u \cos 	heta=3$

Hence, $	an 	heta 	imes u \cos 	heta=36$ or $u \sin 	heta=36$

Range, $R=\frac{u^{2} \sin 2 	heta}{g}=\frac{2 u^{2} \sin 	heta \cos 	heta}{g}$

$=\frac{2(u \sin 	heta)(u \cos 	heta)}{10}=\frac{2 	imes 36 	imes 3}{10}=21.6 \mathrm{m}$

The equation of motion of a projectile is: $y = 12x - \frac{5}{9}{x^2}$. The horizontal component of velocity is $3\ ms^{- 1}$ . Given that $g = 10\ ms^{- 2}$ , .......... $m$ is the range of the projectile .

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