Question

Equation of trajectory of a projectile is given by $y = (8 x - \frac{x^{2}}{5})$ where x and y are in metre. If $g = 10 m / s^{2}$ , time of flight is

Moderate

Solution

General equation of trajectory is
$y = x \tan α - \frac{g x^{2}}{2 u^{2} \cos^{2} α}$
comparing this equation with given equation
$\tan α = 8 and \frac{g \sec^{2} α}{2 u^{2}} = \frac{1}{5} \Rightarrow \frac{g (1 + \tan^{2} α)}{2 u^{2}} = \frac{1}{5}$
$∴ u^{2} = \frac{5 \times 10 \times (1 + 8^{2})}{2} \Rightarrow u = 5 \sqrt{65} m / s$
$∴ T = \frac{2 u \sin θ}{g} = \frac{2 \times 5 \sqrt{65}}{10} \times \frac{8}{\sqrt{1 + 8^{2}}} \sec = 8 \sec$

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