Question

A marksman fires a rifle horizontally at a target. How far does the bullet drop in flight if the target is 150 m away and the bullet has a muzzle velocity of 500 m/s?

Answer 1

Let's first find the flight time of the bullet from the kinematic equation:

$$x=v_0t,$$

here, $x=150\ m$ is the distance to the target, $v_0=500\ \dfrac{m}{s}$ is the initial velocity of the bullet, t is the flight time of the bullet.

Then, from this equation we can calculate $t$:

$$t=\dfrac{x}{v_0}=\dfrac{150\ m}{500\ \dfrac{m}{s}}=0.3\ s.$$

Finally, from the another kinematic equation we can find the bullet drop:

$$h=\dfrac{1}{2}gt^2=\dfrac{1}{2}\cdot 9.8\ \dfrac{m}{s^2}\cdot (0.3\ s)^2=0.441\ m.$$

Answer:

$h=0.441\ m.$