Q168 / 170 · Manipal (MET) 2016 · Physics

A stone is projected from the ground with velocity $50 \mathrm{~m} / \mathrm{s}$ at an angle $30^{\circ}$ with horizontal. It crosses a wall after 3 s . How far beyond the wall the stone will strike the ground? ( $g=10 \mathrm{~m} / \mathrm{s}^2$ )

  • A
    90.2 m
  • B
    12.5 m
  • Correct answer
    C
    86.5 m
  • D
    $125 \sqrt{3} \mathrm{~m}$

Solution

Time, $\begin{aligned} T & =\frac{2 u \sin \theta}{g} \\ T & =\frac{2 \times 50 \times \sin 30^{\circ}}{10}\end{aligned}$ $=\frac{2 \times 50 \times \frac{1}{2}}{10}=5 \mathrm{~s}$ Time spent after crossing the wall, $t_2=5-3=2 \mathrm{~s}$ $\begin{aligned}\therefore \text { Distance, } x_2 & =u \cos \theta \times 1_2 \\& =50 \times \cos 30^{\circ} \times 2\end{aligned}$ $\begin{aligned} & =50 \times \frac{\sqrt{3}}{2} \times 2 \\ & =50 \sqrt{3}\end{aligned}$ $\begin{aligned} & =50 \times 1.73 \\ & =86.5 \mathrm{~m}\end{aligned}$

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

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