A baseball is projected with a velocity $v$ making an angle $θ$ with the incline of indication $a$ as shown in figure. Find the condition that the ball hits the incline at right angle.

cot θ = 2 tan a

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sin θ = cos a

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tan θ = sin a

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cot θ = cos a

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Solution

The correct option is A $cot θ = 2 tan a$
$a_{x} = - g s i n α^i u_{x} = v c o s θ^i a_{y} = - g c o s α^j u_{y} = v s i n θ^j T = \frac{2 v s i n θ}{g c o s α} f o r t h e p a r t i c l e t o h i t p e r p e n d i c u l a r v_{x} = 0 v c o s θ - (g s i n α) T = 0 \Rightarrow v c o s θ = g s i n α \frac{2 v s i n θ}{g c o s α} \Rightarrow c o t θ = 2 t a n α$

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