Question

The Barangay council of San Jose will conduct a fireworks display on the evening of December 24. As part of the organizing team, you have to make sure that the firework residue (assuming it will make a parabolic path) will not land on the viewer's area which is 25 m away. If each of the fireworks will be launched at a constant initial velocity of 30m/s. at what angle must you suggest the Head Organizer to fill the fireworks to avoid it from landing on the people watching?

Answer 1

Let's write the range of the fireworks:

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

From this formula, we can find the launch angle of the fireworks:

$$sin2\theta=\dfrac{Rg}{v_0^2},$$ $$2\theta=sin^{-1}(\dfrac{Rg}{v_0^2})=sin^{-1}(\dfrac{25\ m\cdot 9.8\ \dfrac{m}{s^2}}{(30\ \dfrac{m}{s})^2})=15.8^{\circ},$$ $$\theta=\dfrac{15.8^{\circ}}{2}=7.9^{\circ}.$$

Answer:

To avoid the fireworks from landing on the people watching, the launch angle should be

less than $7.9^{\circ}$.