Projectile Motion Without Resistance
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A particle is projected from \(O\) at an angle of \(\theta\) with a velocity of \(V\) metres per second. The particle lands at a distance of \(R\) metres from the origin at time \(T\). The equations of motion of the particle are \(\ddot{x} = 0\) and \(\ddot{y} = -g\).
(i) Using calculus, derive the expressions for the position of the particle at time \(t\).
(ii) Show that \(\tan\theta = \dfrac{gT^2}{2R}\).
(iii) Show that \(R = \dfrac{V^2\sin 2\theta}{g}\).
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