Final answer:
Physics principles of projectile motion are used to calculate the height at which a firework explodes, utilizing the vertical component of the initial velocity and the acceleration due to gravity. The formula H = Voy² / (2g) gives the maximum height, and large fireworks typically explode at heights allowing for broad visibility.
Step-by-step explanation:
When calculating the height at which a firework explodes, we can use physics principles that relate to projectile motion. Using the initial speed (70.0 m/s) and launch angle (75.0°) given in the question, we can determine the vertical component of the velocity (Voy). Since the firework explodes at its highest point, the vertical velocity component will be zero at this point due to gravity's effect.
To find the maximum height (H), we start with the formula for vertical motion:
H = Voy² / (2g)
where Voy is the initial vertical velocity and g is the acceleration due to gravity (approximately 9.81 m/s²). First, we calculate the initial vertical velocity (Voy) using the formula Voy = V * sin(θ), where V is the initial speed and θ is the launch angle. In this case, Voy = 70.0 m/s * sin(75.0°).
Once we have Voy, we can substitute it into the formula for H to find the maximum height. Note that in our calculations, we assume that air resistance is negligible. Typically, large fireworks reach significant heights, which is consistent with the calculated values from these principles.
For a more detailed solution, one would have to complete the calculations. However, based on similar examples, we can deduce that the height at which large fireworks explode is considerable, often over 200 meters, allowing visibility from a great distance.