Problema Solution
an arrow is shot into the air with an upward velocity of 80 ft per second. The height of the arrow ,h(T) in terms of time since the arrow was released, t is h(t)=80t-16t^2. How long does it take the arrow to reach its maximum height? What is the greatest height the arrow reaches
Answer provided by our tutors
We need to find the vertex of the parabolic function:
h(t)=80t-16t^2
t max = -b/2a, where a = -16, b = 80, c = 0
t max = -80/(2*(-16))
t max = 2.5 s
h max = c - b^2/(4a)
h max = 0 - 80^2/(4*(-16))
h max = 100 ft
The arrow takes 2.5 seconds to reach the maximum height of 100 feet.