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?

Firework A

360 ft/s

Firework B

340 ft/s

Answer 1

Answer:

both fireworks will explode 4.5 seconds after  Firework B launches

Step-by-step explanation:

Given;

speed of firework A, $V_A$= 360 ft/s

speed of firework B, $V_B$ = 340 ft/s

If the two fireworks explodes at the same height, then the height attained by the two fireworks are equal.

let the distance traveled by each firework before explosion = d

Distance = speed x time

Distance A = Distance B

speed A x time = speed B x time

let the time both fireworks explodes after Firework B launches = t

($V_A$) t = ($V_B$ ) t

360t = 340t

if firework B is launched 0.25 s before Firework A, for the time of the two fireworks to be equal since we are considering time (t) after 0.25 seconds, we will have;

360(t-0.25) = 340t

360t  - 90 = 340t

360 t - 340 t = 90

20 t = 90

t = 90/20

t = 4.5 seconds

Therefore, both fireworks will explode 4.5 seconds after  Firework B launches