A particle is projected from the ground with velocity u at angle q with horizontal. The horizontal range, maximum height and time of flight are R, H and T respectively. They are given by, $R= \frac{u^{2} sin 2θ}{g}, H= \frac{u^{2} \sin^{2} θ}{2 g} and T = \frac{2 u \sin θ}{g}$
Now keeping u as fixed q is varied from 30° to 60°. Then:

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R will first increase. H will increase and T will decrease

R will first increase then decrease while H and T both will increase

R will increase while H and T will decrease

R will decrease while H and T will increase

answer is B.

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Detailed Solution

$\begin{array}{l} Range→ R α \sin 2 θ h e r e \sin 2 θ w i l l f i r s t i n c r e a s e t i l l 45^{0} t h e n d e c r e a s e \\ maximum height \to H α \sin^{2} θ h e r e \sin^{2} θ will only increase. \\ t i m e o f f l i g h t \to T α \sin θ h e r e \sin θ will only increase. \end{array}$