Question

The polynomial –16t2 + 200t represents the height, in feet, of a model rocket t seconds after launch. The rocket contains a small firecracker that explodes 6.25 s after launch. Jeremy launches the rocket straight up into the air. If sound travels at about 1144 ft/s, how many seconds after launch will Jeremy hear the firecracker go off?

Answer 1

6.25 seconds after launch the rocket is at height -16(6.25)^2 + 200(6.25) = 625 feet.
It takes 625/1144 = 0.546 seconds for sound to travel 625 feet.
So the total length of time between the launch and the sound reaching the ground is:
6.25 + 0.546 = 6.8 seconds

Answer 2

Thanks!!