Question

The muzzle velocity of bullets fired by German made military assault rifle G3 is 1790 mi/h. If the rifle is fired from a height of 5 ft parallel to the ground, determine the range of that bullet.

Answer 1

First of all, let us convert the given data into the standard units.

Velocity = 1790 mi/h

$\begin{gathered} v=1790\times\frac{1\; km}{1.609\; \text{mile}}\times\frac{1000\; m}{1\; km}\times\frac{3600\; s}{1\; \text{hour}} \\ v=1790\times\frac{1000\cdot3600}{1.609} \\ v=800\; \frac{m}{s} \end{gathered}$

The bullet was fired from a height of 5 ft.

$\begin{gathered} s=5\times\frac{12\; in}{1\; ft}\times\frac{2.54\; cm}{1\; in}\times\frac{1\; m}{100\; cm} \\ s=5\times\frac{12\times2.54}{100} \\ s=1.524\; m \end{gathered}$

Now, we need to find out the time it takes for the bullet to reach the ground.

$s=u\cdot t+\frac{1}{2}gt^2$

Where g is the acceleration due to gravity and u is the initial velocity of the bullet which must be zero since the bull was at rest initially.

$\begin{gathered} s=u\cdot t+\frac{1}{2}gt^2 \\ 1.524=0\cdot t+\frac{1}{2}\cdot9.81\cdot t^2 \\ 1.524=\frac{1}{2}\cdot9.81\cdot t^2 \\ t^2=\frac{2\cdot1.524}{9.81} \\ t^2=0.311 \\ t=\sqrt[]{0.311} \\ t=0.558\; s \end{gathered}$

The horizontal distance covered by the bullet is given by

$\begin{gathered} d=v\cdot t \\ d=800\cdot0.558 \\ d=446.4\; m \end{gathered}$

Therefore, the range of the bullet is 446.4 m

Or 1464.6 ft