MCQ
A particle is projected from the ground with velocity $u$ at angle $\theta$ with horizontal. The horizontal range, maximum height and time of flight are $R, H$ and $T$ respectively. They are given by $R = \frac{{{u^2}\sin 2\theta }}{g}$, $H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and $T = \frac{{2u\sin \theta }}{g}$  Now keeping $u $ as fixed, $\theta$ is varied from $30^o$ to $60^o$. Then,
  • A
    $R$ will first increase then decrease, $H$ will increase and $T$ will decrease
  • $R$ will first increase then decrease while $H$ and $T$ both will increase
  • C
    $R$ will decrease while $H$ and $T$ will increase
  • D
    $R$ will increase while $H$ and $T$ will increase

Answer

Correct option: B.
$R$ will first increase then decrease while $H$ and $T$ both will increase
b
$R \propto \sin 2 \theta, H \propto \sin ^{2} \theta$ and $T \propto \sin \theta, \sin 2 \theta$ will first increase, then decrease. While sin $\theta$ will only increase.

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