Firework A goes off at 320ft/s firework b goes off at 220ft/s but firework b is launched 0.25s before A
What is your question?
To compare the heights at which Firework A and Firework B go off, we need to consider their velocities and the time difference between their launches.
1. Calculate the height of Firework A:
Firework A has a velocity of 320 ft/s. Let's assume it goes off at time t. So, the height of Firework A (hA) can be calculated using the formula:
hA = 320t
2. Calculate the height of Firework B:
Firework B has a velocity of 220 ft/s. However, it is launched 0.25 seconds before Firework A. So, to find the height of Firework B (hB) at time t, we need to consider the time difference.
Firework B will have reached a height slightly earlier than t, so the time for Firework B can be expressed as (t - 0.25). Therefore, the formula for Firework B is:
hB = 220(t - 0.25)
3. Compare the heights of Firework A and Firework B:
Since Firework B is launched earlier, we need to find the time (t) when both Firework A and Firework B will reach the same height. This means hA = hB:
320t = 220(t - 0.25)
Now, solve the equation:
320t = 220t - 55
100t = 55
t = 0.55 seconds
Therefore, Firework A and Firework B will reach the same height after approximately 0.55 seconds. We can plug this value back into the height formulas to calculate the actual heights at this time.