The equation for the trajectory of a projecti | vedclass

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(D) The general equation of the trajectory of a projectile is given by $y = x 	an 	heta - \frac{g x^2}{2 u^2 \cos^2 	heta}$.Comparing this with the

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$20$

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(D) The general equation of the trajectory of a projectile is given by $y = x 	an 	heta - \frac{g x^2}{2 u^2 \cos^2 	heta}$.Comparing this with the given equation $y = \frac{x}{\sqrt{3}} - \frac{x^2}{60}$:$1$. Comparing the coefficient of $x$: $	an 	heta = \frac{1}{\sqrt{3}} \Rightarrow 	heta = 30^{\circ}$.$2$. Comparing the coefficient of $x^2$: $\frac{g}{2 u^2 \cos^2 	heta} = \frac{1}{60}$.Substituting $g = 10 	ext{ m s}^{-2}$ and $	heta = 30^{\circ}$:$\frac{10}{2 u^2 \cos^2 30^{\circ}} = \frac{1}{60} \Rightarrow \frac{5}{u^2 (\sqrt{3}/2)^2} = \frac{1}{60}$.$\frac{5}{u^2 (3/4)} = \frac{1}{60} \Rightarrow \frac{20}{3 u^2} = \frac{1}{60}$.$3 u^2 = 1200 \Rightarrow u^2 = 400$.$u = 20 	ext{ m s}^{-1}$.

The equation for the trajectory of a projectile is $y = \left( \frac{x}{\sqrt{3}} - \frac{x^2}{60} \right) \text{ m}$. The velocity of projection of the projectile is (Acceleration due to gravity $g = 10 \text{ m s}^{-2}$) (in $\text{ m s}^{-1}$)

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