Question

Range of a cannon ball. Suppose one of Napoleon’s cannons had a muzzle speed, vi, of 60 m/s. At what angle should it have been aimed (ignore air resistance) to strike a target 320 m away?

Answer 1

The length of flying for the body launched at the angle $\alpha$ with the initial speed $v_0 = 60m/s$ is (see https://opentextbc.ca/universityphysicsv1openstax/chapter/4-3-projectile-motion/):

$$L = \dfrac{v_0^2\sin2\alpha}{g}$$

where $g = 9.81m/s^2$ is the gravitational acceleration. Expressing $\alpha$, obtain:

$$\alpha =\dfrac{1}{2}\arcsin \left( \dfrac{Lg}{v_0^2}\right)$$

If $L = 320m$, then:

$$\alpha =\dfrac{1}{2}\arcsin \left( \dfrac{320\cdot 9.81}{60^2}\right) \approx 30.3\degree$$

Answer. $30.3\degree$.