Question

A spring-loaded gun can fire a projectile to a height h if it is fired straight up. if the same gun is pointed at an angle of 30° from the vertical, what maximum height can now be reached by the projectile

Answer 1

The maximum height

$$h_{max}=\frac{v_y^2}{2g}$$

In the first case, when projectile is fired straight up

$$h=\frac{v_0^2}{2g}$$

In the second case, when projectile is fired at an angle of 30° from the vertical

$$h_{max}=\frac{(v_0\cos 30^\circ)^2}{2g}=\frac{(v_0\times \sqrt{3}/2)^2}{2g}=\frac{3}{4}h$$