Question

Find the minimum initial speed of a cork that pops out of a bottle and which travels a horizontal distance of 10 m.

Answer 1

The range for the projectile motion

$$R=\frac{v_0^2\sin2\theta}{g}.$$

The maximum range for the projectile motion ($\theta=\pi/4$ )

$$R_{\rm max}=\frac{v_0^2}{g}.$$

Hence

$$v_0=\sqrt{gR_{\rm max}}=\sqrt{10\times 10}=10\:\rm m/s.$$