Respuesta :
Answer:
The second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare
Step-by-step explanation:
The given parameters are;
The height of the first flare = 196 feet
The duration the first flare spends in the air = 7 seconds
The function representing the height of the second flair is f(t) = -16t(t - 8)
Where;
t = The time since the passenger shot the second flare
The time the flair stays i the air is given by the time it takes for the height, f(t), to be 0 as follows;
f(t) = 0 = -16t(t - 8)
-16t(t - 8) = 0
t = 0, or t = 8
The time the second flare stays in the air = 8 seconds
The maximum height reached by the second flair is given by the finding the maximum point of the curve of the function as follows;
d(f(t))/dt = 0 = d(-16t(t - 8))/dt = -32t + 128 at the maximum point (the coefficient of t² is negative in the quadratic equation)
-32t + 128 = 0
128 = 32t
32t = 128
t = 128/32 = 4
t = 4 at maximum height and f(4) = -16 × 4 × (4 - 8) = 256 feet
The maximum height reached by the second flare f(4) = -16 × 4 × (4 - 8) = 256 feet.
Therefore, the second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare, with maximum height of 196 feet, and time in the air of 7 seconds.
