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Q.

As shown in the below figure a body is projected up the plane, then the time of flight and maximum range when $β = 0$ are

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a

$T = \frac{2 u \sin α}{g}, R_{\max} = \frac{u^{2}}{g}$

b

$T = \frac{2 u \cos α}{3 g}, R_{\max} = \frac{u}{g}$

c

$T = \frac{2 u \tan α}{g}, R_{\max} = \frac{2 u}{g^{2}}$

d

$T = \frac{2 u \tan α}{g}, R_{\max} = \frac{u^{2}}{g}$

answer is A.

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Detailed Solution

$t i m e o f f l i g h t = T = \frac{2 u \sin (α - β)}{g \cos β} \Rightarrow T = \frac{2 u \sin α}{g} (∵ β = 0) m a x i m u m r a n g e = R_{m a x} = \frac{u^{2} \sin 2 θ}{g} \Rightarrow R_{m a x} = \frac{u^{2}}{g} (\sin 2 θ = 1 f o r \max i m u m)$

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