The equations of motion of a projectile are g | vedclass

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(A) The given equations are $x = 36 t$ and $2 y = 96 t - 9.8 t^2$. Dividing the second equation by $2$,we get $y = 48 t - 4.9 t^2$. Comparing these wi

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$\sin^{-1}(\frac{4}{5})$

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(A) The given equations are $x = 36 t$ and $2 y = 96 t - 9.8 t^2$. Dividing the second equation by $2$,we get $y = 48 t - 4.9 t^2$. Comparing these with the standard equations of projectile motion: $x = (u \cos 	heta) t$ and $y = (u \sin 	heta) t - \frac{1}{2} g t^2$. We identify $u \cos 	heta = 36$ and $u \sin 	heta = 48$. To find the angle of projection $	heta$,we calculate $	an 	heta = \frac{u \sin 	heta}{u \cos 	heta} = \frac{48}{36} = \frac{4}{3}$. Since $	an 	heta = \frac{4}{3}$,we can construct a right-angled triangle with opposite side $4$ and adjacent side $3$. The hypotenuse is $\sqrt{4^2 + 3^2} = 5$. Therefore,$\sin 	heta = \frac{	ext{opposite}}{	ext{hypotenuse}} = \frac{4}{5}$. Thus,$	heta = \sin^{-1}(\frac{4}{5})$.

List-$I$	List-$II$
$A$. Butane $\to$ Isobutane	$a$. Cracking
$B$. Butane $\to$ Lower hydrocarbons	$b$. Isomerisation
$C$. $n$-Heptane $\to$ Toluene	$c$. Reed reaction
$D$. Propane $\to$ $CH_3CH_2CH_2SO_2Cl$	$d$. Aromatisation

The equations of motion of a projectile are given by $x = 36 t$ metre and $2 y = 96 t - 9.8 t^2$ metre. The angle of projection is:

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