Tower Attack

Overview

A cannon must hit a tower located at a specific distance $d$ on the same horizontal level. The cannon fires a projectile with a fixed initial speed $v_0$.

Calculate and set the correct launch angle $\theta$ so the projectile hits the target.

If the angle is incorrect, the projectile will either fall short or overshoot the tower.

Relevant Equations

$$x(t) = x_0+v_{0x}t$$ $$v_y(t) = v_{0y} + a_y t$$ $$v_{0x} = v_0\cos\theta$$ $$v_{0y} = v_0\sin\theta$$ $$2\sin\theta\cos\theta = \sin2\theta$$