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A projectile is thrown with an initial v...

A projectile is thrown with an initial velocity of `v = a hat i + b hat j`. If the range of projectile is double the maximum height reached by it. Find the ratio `(b)/(a)`.

Text Solution

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Angle of projection, `theta = tan^-1 ((v_y)/(v_x)) = tan^-1 ((b)/(a)) :. Tan theta = (b)/(a)` …(i)
From formula : `R = 4 H cot theta = 2 H`
`rArr cot theta = (1)/(2) :. Tan theta = 2` `[As R = H given]`…(ii)
From Eqs (i) and (ii), `b = 2a`.
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