Kinematics

JEE Main level, single correct, medium

266 of 308

Question 266 of 308

The initial speed of a bullet fired from a rifle is 630 m/s630 \mathrm{~m} / \mathrm{s}. The rifle is fired at the centre of a target 700 m700 \mathrm{~m} away at the same level as the target. How far above the centre of the target ?

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Answer: (C) 6.1 m6.1 \mathrm{~m}

Let ' tt ' be the time taken by the bullet to hit the target.
∴700 m=630 ms−1t⇒t=700 m630 ms−1=109sec\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=0u=0
∴h=12gt2=12×10×(109)2\begin{aligned} &\therefore h=\frac{1}{2} g t^2 \\ &=\frac{1}{2} \times 10 \times\left(\frac{10}{9}\right)^2 \end{aligned}
=50081 m=6.1 m=\frac{500}{81} \mathrm{~m}=6.1 \mathrm{~m}
Therefore, the rifle must be aimed 6.1 m6.1 \mathrm{~m} above the centre of the target to hit the target.

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