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

Correct answer: C. 6.1 ~m Let ' t ' be the time taken by the bullet to hit the target. aligned & 700 ~m=630 ~ms^ -1 t & t= 700 ~m 630 ~ms^ -1 =(10)/(9) sec aligned For vertical motion, Here, u=0 aligned & h=(1)/(2)g t² &=(1)/(2) ×10 ×((10)/(9))^2 aligned = (500)/(81) ~m= 6.1 ~m Therefore, the rifle must be aimed 6.1 ~m above the centre of the target to hit the target.

JEE Main 201411 AprilOnline

Exam: JEE Main
Year: 2014
Date: 11 April
Mode: Online
Subject: Physics
Chapter: Motion in Two Dimensions

JEE Main 2014 · 11 April · Online · Physics · Motion in Two Dimensions

The initial speed of a bullet fired from a rifle is 630 ~m / s ....

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 ?

Options

A $1.0 \mathrm{~m}$
B $4.2 \mathrm{~m}$
C $6.1 \mathrm{~m}$
D $9.8 \mathrm{~m}$

Correct answer

C. $6.1 \mathrm{~m}$

Step-by-step 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 t² \\ &=\frac{1}{2} \times10 \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.

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