Q123 / 160 · TS EAMCET 2004 · Physics

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x=6 t$ metre and $y=8 t-5 t^2$ metre. The range of the projectile in metre is

  • Correct answer
    A
    $9.6$
  • B
    $10.6$
  • C
    $19.2$
  • D
    $38.4$

Solution

$$ \begin{aligned} & x=(u \cos \theta) t=6 t \\ & \quad y=(u \sin \theta) t-\frac{1}{2} g t^2=8 t-5 t^2 \end{aligned} $$ Therefore, $u \sin \theta=8$ $u \cos \theta=6$ $\begin{aligned} Range\ R & =\frac{u^2 \sin 2 \theta}{g}=\frac{u^2 \times 2 \sin \theta \cos \theta}{g} \\ & =\frac{2(u \sin \theta)(u \cos \theta)}{g} \\ & =\frac{2(8)(6)}{10}=9.6 \mathrm{~m}\end{aligned}$

Hence, the correct answer is option: 'A'.

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