SOLUTION: A boy is standing next to the chimney on top of the roof of a house, which is located on the top of a cliff. The chimney runs straight down into the fireplace at the floor of the b

Question 603039: A boy is standing next to the chimney on top of the roof of a house, which is located on the top of a cliff. The chimney runs straight down into the fireplace at the floor of the basement of the house. The cliff on which the house is built rises 50 feet above the ocean below. The roof of the house is 18 feet above the ground on which it is built, and the floor of the basement is 9 feet below ground. He throws a ball straight upward with an initial velocity of 80 feet per second. At the moment the ball is released, the boy's hand is level with the top of the chimney 5 feet above the roof. From this information, it can be shown that the height h of the ball t seconds after it is released from the boy's hand is modeled by the following equation:
h(t)= -16t2 + 80t +73
to the nearest tenth of a second, determine the amount of time after the ball is released from the boy'y hand at which it lands in the fireplace in the basement of the house.
Found 2 solutions by stanbon, nerdybill:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
h(t)= -16t2 + 80t +73
======
-16t^2 + 80t+73 = -9
---
-16t^2 + 80t + 82
------------------------
t = [-80 +- sqrt(80^2-4*(-16)*82)]/(-32)
---
t = 5.8727 seconds
=======================
Cheers,
Stan H.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Given equation:
h(t)= -16t2 + 80t +73
.
The basement floor (relative to sea level) is 50-9 = 41 feet
.
Set h(t) to 41 and solve for t:
h(t)= -16t2 + 80t +73
41 = -16t2 + 80t +73
0 = -16t2 + 80t + 114
0 = -8t2 + 40t + 57
0 = 8t2 - 40t - 57
Solve by the "quadratic formula" to get:
x = {6.2, -1.2}
throw out the negative solution (extraneous) leaving:
x = 6.2 seconds
.
details of quadratic formula:

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=3424 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.15718470958195, -1.15718470958195. Here's your graph:

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