They plan for two fireworks to explode at the same height in the air. They travel at 320 ft/s(Firework A) and 240 ft/s (Firework b). Firework B is launched 0.25 s before Firework A.

Question

How many seconds after Firework B launches will both fireworks​ explode?

Answer 1

Firework B has a 0.25s headstart with a speed 240ft/s. The headstart distance for B is therefore, 60ft (= 240 * 0.25). Note, that we are assuming the effect of gravitational acceleration is negligible. In practice, the rocket will slow down due to force of gravity.

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Firework A is then launched. Assume that it explodes after time t.

Distance traveled by rocket A = 320*t

This distance must be equal to the sum of the headstart distance for B, AND the additional distance B travels in time 't'. So

320*t = 60 + 240*t

Solve this to obtain

t = 0.75s

To answer the question asked "How many seconds after Firework B launches will both fireworks​ explode?" you must add the 0.25s headstart given to B. So the answer is

Time = 1.0s after B was fired.

Answer 2

B is fired first and after 0.25 seconds, reaches 60 feet

Then A is fired and 320t = 240t + .25, then 80t =.25, after t = 0.003125 seconds they both explode or at 81 feet.