Question

The path followed by a body projected along y-axis is given as by $y = \sqrt{3} x - (1 / 2) x^{2}, if g = 10 m / s^{2}$ , then the initial velocity of projectile is (x and y are in m).

Moderate

Solution

On comparing the coefficient of x² in the given equation with the standard equation, we get
$\begin{array}{l} y = xtan θ - \frac{{gx}^{2}}{2 u^{2} \cos^{2} θ}, \tan θ = \sqrt{3}; θ = 60^{0} \\ \Rightarrow \frac{g}{2 u^{2} \cos^{2} θ} = \frac{1}{2} \end{array}$
Substituting $θ = 60^{\circ}, we get u = 2 \sqrt{10} m / s$

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