H(t)=-16t^2+80t+7

Question

A set of fireworks mortar shells is launched from the staging platform at 80 ft/sec from an initial height of 7 ft above the ground. The height of the fireworks, h(t), can be modeled by

h(t)=-16t^2+80t+7

where t is the time in seconds after the launch. Round answers to three decimal places.

A) for how many seconds after the launch would the fuses need to be set so that the mortar shells would in fact explode at the maximum height?

the fireworks will reach their maximum heigh in _______ sec.

B) what is the height of the fireworks when at maximum heigh?

Answer 1

A=-16 B=80 C=7

max is -b/(2a) = -80/(2*-16) = -80/-32 = 40/16 = 20/8 = 10/4 = 5/2

Max occurs at 5/2 = 2.5 seconds

-16(2.5)^2 +80(2.5) + 7 =

-16(6.25) + 200 + 7 = 107.375