Question

A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below, (firework A: 340 ft/s, firework B: 320 ft/s) Firework B is launched 0.25 s before Firework A. How many seconds after Firework B launches will both fireworks​ explode?

Answer 1

After Firework B launches, it will take Firework A approximately 0.235 seconds to catch up, and both fireworks will explode at that time.

Step-by-step explanation:

In order to determine the time at which both fireworks will explode, we need to calculate the time it takes for firework A to catch up to firework B. Firework B is launched 0.25 s before Firework A, so we need to find the time it takes for Firework A to cover the distance that Firework B traveled in 0.25 s.

The distance covered by Firework B in 0.25 s is 320 ft/s * 0.25 s = 80 ft.

Now, we need to find the time it takes for Firework A to cover an 80 ft distance with a speed of 340 ft/s. Using the formula time = distance / speed, we find that the time it takes for Firework A is 80 ft / 340 ft/s = 0.235 s.

Therefore, after Firework B launches, it will take Firework A approximately 0.235 seconds to catch up, and both fireworks will explode at that time.