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Question: A projectile is thrown with an initial velocity of \(v = a\widehat{i} + b\widehat{j},\) if the range...

A projectile is thrown with an initial velocity of v=ai^+bj^,v = a\widehat{i} + b\widehat{j}, if the range of projectile is double the maximum height reached by it then

A

a = 2b

B

b = a

C

b = 2a

D

b = 4a

Answer

b = 2a

Explanation

Solution

Angle of projection θ=tan⁡−1vyvx=tan⁡−1ba\theta = \tan^{- 1}\frac{v_{y}}{v_{x}} = \tan^{- 1}\frac{b}{a}

∴ tan⁡θ=ba\tan\theta = \frac{b}{a} …(i)

From formula R=4Hcot⁡θ=2HR = 4H\cot\theta = 2H ⇒ cot⁡θ=12\cot\theta = \frac{1}{2}

∴ tan⁡θ=2\tan\theta = 2 …(ii) [As R = 2H given]

From equation (i) and (ii) b = 2a