Question

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

Answer 1

3.25 seconds after B launches

Explanation:

In the 0.25 seconds before A launches, B will have traveled ...

distance = speed · time

distance = (240 ft/s)(0.25 s) = 60 ft

The speed of A is 20 ft/s faster, so will close that 60 ft gap at the rate of 20 ft/s. It will take ...

time = distance/speed

time = 60 ft/(20 ft/s) = 3 s

The fireworks will be at the same height 3 seconds after A is launched. That is 3.25 seconds after B is launched.

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Additional comment

Their heights will be (3 s)(260 ft/s) = 780 ft = (3.25 s)(240 ft/s).