Trajectories
PART I
The path a firework traces in the air is called its trajectory. If the trajectory isn’t perfectly planned the firework might explode in the wrong place and ruin the show or even hurt someone. In this activity you are going to design a trajectory so that the firework explodes at the perfect height and distance.
We begin by studying the motion of fireworks in the horizontal (x) direction.
There are a few variables pyrotechnicians must consider when calculating how far the shell will travel. Friction due to the air will slow the shell down, and wind will also affect its trajectory. In our analysis we will neglect these affects, but keep them in mind as professionals must always take into account.
The equation for the horizontal distance of an object shot from the ground is:
Equation#1
x |
= | horizontal distance |
|---|---|---|
vox |
= | initial horizontal velocity (m/s). The o is a naught symbol, it means initial.The x means horizontal, hence this is the speed of the shell in the horizontal direction when it is fired. |
t |
= | time (s) |
Question #1
a) If you were to graph Equation# 1 what would it look like?
b) If you fire a shell with an initial horizontal velocity of 16m/s, in 15s how far (horizontally) is it from its launch tube?
c) If a shell is in the air for 30 seconds, and it travels 200m horizontally, what was its initial velocity? *to 2 decimal places
