The path of a projectile is given by the equa | vedclass

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(D) The given equation of the trajectory is $y = ax - bx^2$.The standard equation of a projectile trajectory is $y = x 	an 	heta - \frac{gx^2}{2u^2

Vedclass · Accepted Answer

$\frac{a^2}{4b}, 	an^{-1}(a)$

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(D) The given equation of the trajectory is $y = ax - bx^2$.The standard equation of a projectile trajectory is $y = x 	an 	heta - \frac{gx^2}{2u^2 \cos^2 	heta}$.Comparing the coefficients of $x$ and $x^2$ in both equations:$	an 	heta = a \implies 	heta = 	an^{-1}(a)$.Also, $b = \frac{g}{2u^2 \cos^2 	heta}$.The maximum height $H$ is given by $H = \frac{u^2 \sin^2 	heta}{2g}$.From $	an 	heta = a$, we have $\sin 	heta = \frac{a}{\sqrt{1+a^2}}$ and $\cos 	heta = \frac{1}{\sqrt{1+a^2}}$.Substituting $u^2 = \frac{g}{2b \cos^2 	heta}$ into the height formula:$H = \frac{g}{2b \cos^2 	heta} \cdot \frac{\sin^2 	heta}{2g} = \frac{	an^2 	heta}{4b} = \frac{a^2}{4b}$.Thus, the maximum height is $\frac{a^2}{4b}$ and the angle of projection is $	an^{-1}(a)$.

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