Write an equation that represents the path of a firework that is launched from the ground with the initial velocity that you chose.

Question

(Choose whatever initial velocity and consider where that fits into the equation… this time you are launching the firework from the ground so consider how that changes the equation)

Answer 1

To represent the path of a firework launched from the ground with an initial velocity, we can use the equation for vertical motion.

Let's assume the firework is launched upward with an initial velocity of v₀ m/s:

The equation for vertical motion is:
h(t) = v₀t - (1/2)gt²

Where:
- h(t) represents the height of the firework at time t,
- v₀t represents the initial upward velocity multiplied by time,
- g represents the acceleration due to gravity (approximately 9.8 m/s²),
- (1/2)gt² represents the effect of gravity pulling the firework downward over time.

Since we launched the firework from the ground, its initial height is 0. Therefore, we can simplify the equation as:

h(t) = v₀t - (1/2)gt²

This equation represents the path of a firework launched from the ground with an initial velocity of v₀.