Question

the height h of a football launched from a roman candle with an initial velocity of 64 feet per second is given by the equation $h = -16t^2 + 64t$, where t is time in seconds after launch. use the graph of this function to answer the questions.

(a) estimate the maximum height of the football

the maximum height of the football is \boxed{64} ft

(b) estimate the time when the football is at its maximum height

the time when the football is at its maximum height is $t = \boxed{2}$ sec

(c) estimate the time when the football returns to the ground

the time when the football returns to the ground is $t = \boxed{}$ sec

Explanation:

Step1: Set height to 0 (ground level)

$0 = -16t^2 + 64t$

Step2: Factor the quadratic equation

$0 = -16t(t - 4)$

Step3: Solve for t

$-16t=0 \implies t=0$; $t-4=0 \implies t=4$

Step4: Select non-launch time

We discard $t=0$ (launch time), so use $t=4$.

Answer:

The time when the fireball returns to the ground is $t=4$ sec