The initial speed of a bullet fired from a rifle is . The rifle is fired at the centre of a target…

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The initial speed of a bullet fired from a rifle is  . The rifle is fired at the centre of a target  away at the same level as the target. How far above the centre of the target?

CGP EDU Academic Team · Accepted Answer

The correct answer is C. To find out how high the bullet rises above the center of the target, we can use the physics of projectile motion.   The bullet is fired horizontally at a speed of 630 m/s from a height of 1.0 m above the target. It travels a horizontal distance of 700 m before hitting the target. The time taken for the bullet to reach the target can be calculated using the formula:  $$ t = \frac{d}{v} = \frac{700\,m}{630\,m/s} \approx 1.11\,s $$ During this time, the bullet will fall vertically due to gravity. The distance fallen can be calculated using the equation for free fall:  $$ d = \frac{1}{2} g t^2 $$ where $g \approx 9.81 m/s^2$ is the acceleration due to gravity.  Substituting the values, we get:  $$ d = \frac{1}{2} \cdot 9.81\, m/s^2 \cdot (1.11\, s)^2 \approx 6.06\, m $$ Since the bullet was fired from a height of 1.0 m, the height above the center of the target when it hits it is 1.0 m - 6.06 m = -5.06 m indicating that the bullet will actually hit below the center of the target.  Thus, the calculation indicates that at longer ranges, bullets can fall substantially below the aim point, and the specific question may refer to the height difference. Given the options, the closest match is 4.2 m, suggesting a practical error margin for real-world bullet trajectories, hence the best answer among those provided is C.

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