Final answer:
The maximum headwind allowed for firing Smoke Grenades is not explicitly provided, but it is related to the concepts of projectile motion and air resistance which can affect the trajectory and distance traveled by a projectile.
Step-by-step explanation:
The question seems to pertain to the principles of physics, focusing on projectile motion and its application to real-life scenarios involving launching objects, like fireworks or grenades, but specifically relates to a situation not clearly defined in the provided context. The maximum headwind allowed for firing Smoke Grenades is not directly mentioned in the example provided. Instead, the example discusses a fireworks display where a projectile (shell) is launched into the air. Air resistance and other factors, such as wind, could impact the travel distance and explosion point of a projectile.
When launching a projectile, in this case, a firework shell, with an initial speed of 70.0 m/s at an angle of 75.0° above the horizontal, air resistance plays a role in the ultimate height and distance traveled. Without air resistance, a vertical component of initial velocity at 67.6 m/s would allow the projectile to reach a height of 233 m. However, headwinds or gusts of wind can reduce this distance. In practical terms, if a smoke grenade were to be used, the maximum headwind would depend on the specific design, weight, and aerodynamics of the grenade, as well as the desired outcome (height and distance).