SOLUTION: At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air. The height in feet h(t) of the ball at t seconds is given by the formula H(t) = -16t^2 + 96t +

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Question 337633: At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air. The height in feet h(t) of the ball at t seconds is given by the formula
H(t) = -16t^2 + 96t +56
a)How tall is the building (hint: t=0)
b)When is the ball at its highest point?
c)To what height does the ball travel?
d)When does the ball strike the ground?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air. The height in feet h(t) of the ball at t seconds is given by the formula
H(t) = -16t^2 + 96t +56
a)How tall is the building (hint: t=0)
H(t) = -16t^2 + 96t +56
H(0) = -16(0)^2 + 96(0) +56
H(0) = 0 + 0 +56
H(0) = 56 feet
.
b)When is the ball at its highest point?
find the "axis of symmetry":
t = -b/(2a) = -96/(2*(-16)) = -96/(-32) = 3 secs
.
c)To what height does the ball travel?
set t=3:
H(t) = -16t^2 + 96t +56
H(3) = -16(3)^2 + 96(3) +56
H(3) = -16(9) + 96(3) +56
H(3) = -144 + 288 +56
H(3) = 200 feet
.
d)When does the ball strike the ground?
Set H(t)=0 and solve for t:
H(t) = -16t^2 + 96t +56
0 = -16t^2 + 96t +56
Dividing both sides by 8:
0 = -2t^2 + 12t + 7
Apply quadratic formula to get:
t = {-0.54, 6.54}
Toss out the negative solution to get
t = 6.54 secs
.
Details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=200 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.535533905932738, 6.53553390593274. Here's your graph: