Question

A rifle that shoots bullets at 460 m/s is to be aimed at a target 45.7 m away. If the center of the target is level with the rifle, how high above the target must the rifle barrel be pointed so that the bullet hits dead center

Answer 1

We have:

$$\tan{\theta}=\frac{l}{R}$$

The range is

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

$$45.7=\frac{460^2\sin{2\theta}}{9.8}$$

$$\theta=0.0606\degree$$

Thus,

$$\tan{0.0606\degree}=\frac{l}{45.7}$$

$$l=0.0483\ m$$