Answer:
Max height: 61.25 feet
Max height reached at 15/8 seconds, or 1.875 seconds
How long to hit the ground: (15 + 7√5)/8 or about 3.83 seconds
How high after 1 second: 49 feet
Step-by-step explanation:
Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.
The general form for a quadratic equation is ax² + bx + c,
here a is -16, and b is 60
To find the x coordinate of the vertex, use x = -b/(2a)
We have x = -60/[2(-16)]
x = -60/-32
x = 15/8
So at 15/8 seconds, the ball reaches is maximum height
Now plug that into the equation to find the y value, which will be the height...
y = -16(15/8)² + 60(15/8) + 5
y = -16(225/64) + 900/8 + 5
y = -225/4 + 450/4 + 20/4
y = 245/4
y = 61.25 feet
To find out how long the ball was in flight, solve the equation...
0 = -16t² + 60t + 5
Use quadratic equation...
x = -60/-32 ± √[60² - 4(-16)(5)]/-32
x = 15/8 ± (√3920)/-32
x = 15/8 ± (28√5)/-32
x = 15/8 ± (-7√5)/8
so x = (15 - 7√5)/8 and (15 + 7√5)/8
(15 - 7√5)/8 is negative, and we're talking about time, so this answer is ignored.
(15 + 7√5)/8 seconds is when the ball hits the ground
To find out out how high the ball was after 1 second, plug 1 in for x and simplify
h(1) = -16(1²) + 60(1) + 5
h(1) = -16 + 60 + 5
h(1) = 49
