Answer:
Yes; at 1.75 s; 72.25 ft
Step-by-step explanation:
h = -16t² +68t
a = -16; b = 68; c = 0
The vertex h of a parabola is at
h = -b/(2a) and the maximum height is at
y = f(h)
1. Time to maximum height
[tex]t = -\dfrac{b}{2a} = -\dfrac{68}{2\times(-16)} = \dfrac{68}{32} = \textbf{2.125 s}[/tex]
2. Maximum height
[tex]\text{Height} = f(2.125) = -16(2.125)^{2} + 68(2.125) = -72.25 + 144.5 = \textbf{72.25 ft}[/tex]
3. Does the golf ball reach 70 ft?
Yes, it passes 70 ft on the way to its maximum height of 72.25 ft.
4. Time to 70 ft
-16t² + 68t = 70
-16t² + 68t - 70 = 0
8t² -34t + 35 = 0
( 4t -7) (2t - 5) = 0
4t - 7 = 0 2t - 5 = 0
4t = 7 2t = 5
t = 1.75 s t = 2.5 s
The golf ball reaches 70 ft at 1.75 s on the way up and 2.5 s on the way down.
The diagram below shows the path of your parabola.
