Problema Solution
A ball is thrown directly upward from a height of 30 feet with an initial velocity of 64 feet per second. The equation h=-16t^2+64t+30 gives the height h after the seconds. How long does it take for the ball to reach its maximum height? What is the maximum height of the ball?
Answer provided by our tutors
we need to find the vertex of the parabola
h(t)=-16t^2+64t+30
t max = -b/(2a) the time the ball needs to reach maximum height
h max = c - b^2/(4a) the maximum height of the ball
where a = -16, b = 64, c = 30
t max = -64/(2*(-16))
t max = 2 sec
h max = 30 - 64^2/(2*(-16))
h max = 150 ft
the ball needs 2 seconds to reach maximum height.
the maximum height of the ball is 150 ft.