Question

The initial speed of a bullet fired from a rifle is $630m/s$. The rifle is fired at the center of a target $700m$ away at the same level as the target. How far above the center of the target the rifle must be aimed in order to hit the target? ( Take $g=10m/s^2$ )

• A. $9.8m$
• B. $4.2m$
• C. $1.0m$
• D. $6.17m$

Answer 1

The correct option is D $6.17m$

The question pertains to the concept of projectile motion.

$u=630m/s$ , $R=700m$

Using, the formula for range of a projectile,

$R=\frac{u^2\sin 2\theta }{g}$

$\sin 2\theta =\frac{700\times 10}{630\times 630}$

Thus, $\sin 2\theta =\frac{10}{63\times 9}$

So, $\tan \theta =\frac{6.17}{700}$
Or, the height above which the projectile should be fired is 6.17 m