The initial speed of a bullet fired from a rifle is $630 \mathrm{~m} / \mathrm{s}$. The rifle is fired at…

The initial speed of a bullet fired from a rifle is $630 \mathrm{~m} / \mathrm{s}$. The rifle is fired at the centre of a target $700 \mathrm{~m}$ away at the same level as the target. How far above the centre of the target ?
  1. $1.0 \mathrm{~m}$
  2. $4.2 \mathrm{~m}$
  3. $6.1 \mathrm{~m}$
  4. $9.8 \mathrm{~m}$

Solution

Let ' $t$ ' be the time taken by the bullet to hit the target. $ \begin{aligned} &\therefore \quad 700 \mathrm{~m}=630 \mathrm{~ms}^{-1} t \\ &\Rightarrow t=\frac{700 \mathrm{~m}}{630 \mathrm{~ms}^{-1}}=\frac{10}{9} \mathrm{sec} \end{aligned} $ For vertical motion, Here, $u=0$ $ \begin{aligned} &\therefore h=\frac{1}{2} g t^2 \\ &=\frac{1}{2} \times 10 \times\left(\frac{10}{9}\right)^2 \end{aligned} $ $ =\frac{500}{81} \mathrm{~m}=6.1 \mathrm{~m} $ Therefore, the rifle must be aimed $6.1 \mathrm{~m}$ above the centre of the target to hit the target

Asked in: JEE Main 2014 (11 Apr Online)

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