Projectile motion
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A particle is projected from a point on horizontal ground with speed \(100 \text{ m} / \text{ s}\) at an angle of \(45^{\circ}\) to the horizontal. Let \(i\) and \(j\) be unit vectors in the horizontal \((x)\) and vertical \((y)\) directions respectively. Neglecting air resistance, find:
(Take \(g=10 \text{ m} / \text{ s}^2\)).
i) the initial velocity vector.
ii) the velocity vector at time \(t\) seconds.
iii) the position vector at time \(t\) seconds.
iv) the cartesian equation of the path.
i) \(50 \sqrt{2} i+50 \sqrt{2} j\)
ii) \(50 \sqrt{2} i+(50 \sqrt{2}-10 t) j\)
iii) \(50 \sqrt{2} t i+\left(50 \sqrt{2} t-5 t^2\right) j\)
iv) \(y =x-\frac{x^2}{1000}\)
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