Answer: a) 306.25 feet b) 8 s
Step-by-step explanation:
Actually we have to find the function' s h(t) maximum meaning.
To do that we have to find the corresponding t - let call it t max
As known t max= (t1+t2)/2 where t1 and t2 are the roots of quadratic equation' s
Lets find the roots t1 and t2
-16*t^2+116*t+96=0 divide by 4 each side of the equation
-4*t^2 +29*t+24=0
D=29^2+24*4*4=1225 =35^2
t1=(-29-35)/(-8)=8
t2=(-29+35)/(-8)=-6/8=-3/4=-0.75
t max= (8+(-0.75))= 7,25/2=3.625 s
h max= -16*t max ^2+116*t +96= -16*3.625^2+116*3.625+96=306.25 feet
b) t2=8s is the time when the ball hits the ground.
Answer:
a) 306.25 ft
b) 8 seconds
Step-by-step explanation:
a) The time at the maximum height is found from the equation for the axis of symmetry:
ax^2 +bx +c has axis of symmetry at x=-b/(2a)
For the given equation, the t-value at the vertex is ...
t = -116/(2(-16)) = 3.625 . . . seconds
At that time, the height is ...
h = (-16(3.625) +116)(3.625) +96 = (58)(3.625) +96 = 306.25
The maximum height is 306.25 feet.
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b) The ball will hit the ground when h=0. From the vertex values in the first part, we know we can rewrite the equation in vertex form as ...
h(t) = -16(t -3.625)^2 +306.25
This will be 0 when ...
0 = -16(t -3.625)^2 +306.25
(t -3.625)^2 = 306.25/16
t = 3.625 +√19.140625 = 3.625 +4.375 = 8
The ball will hit the ground after 8 seconds.
