SOLUTION: In a cartoon , a malfunctioning cannon fires a hungry coyote towards the bottom of a cliff with an initial rate of 100 feet per second. If the cliff is 1250 feet tall , how long wi

Question 180053: In a cartoon , a malfunctioning cannon fires a hungry coyote towards the bottom of a cliff with an initial rate of 100 feet per second. If the cliff is 1250 feet tall , how long will it take the coyote to reach the desert floor? (To account for gravity, use the formula d =rt + 16t^2, where d =distance, r = initial rate, and t = time.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
In a cartoon , a malfunctioning cannon fires a hungry coyote towards the bottom of a cliff with an initial rate of 100 feet per second. If the cliff is 1250 feet tall , how long will it take the coyote to reach the desert floor? (To account for gravity, use the formula d =rt + 16t^2, where d =distance, r = initial rate, and t = time.
.
From your problem, you are given:
d = 1250 feet
r = 1000 ft/sec
t is what we're looking for...
.
Plug in the provided values and solve for t:
d =rt + 16t^2
1250 = 1000t + 16t^2
625 = 500t + 8t^2
0 = 500t + 8t^2 - 625
.
Using the quadratic equation, we get:
x = {1.110, -1.126}
.
We can toss out the negative solution leaving us with:
x = 1.110 seconds
.
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=1250064 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.11006261005366, -1.12606261005366. Here's your graph:

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