SOLUTION: I've heard that tossing a coin into a fountain will bring me good luck, so I throw a silver dollar up with a velocity of 5m/sec. and it falls into the fountain 1.3 meters below my

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I've heard that tossing a coin into a fountain will bring me good luck, so I throw a silver dollar up with a velocity of 5m/sec. and it falls into the fountain 1.3 meters below my       Log On


   

Question 338999: I've heard that tossing a coin into a fountain will bring me good luck, so I throw a silver dollar up with a velocity of 5m/sec. and it falls into the fountain 1.3 meters below my hand. How long is the coin in the air?
In this question i just really dont understand how to do quadratic equations when you dont have the acceleration unless its -9.8m/s squared, but really not sure.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
I've heard that tossing a coin into a fountain will bring me good luck, so I throw a silver dollar up with a velocity of 5m/sec. and it falls into the fountain 1.3 meters below my hand. How long is the coin in the air?
In this question i just really dont understand how to do quadratic equations when you dont have the acceleration unless its -9.8m/s squared, but really not sure.
.
Yes, gravity is your acceleration.
.
Applying the equation of motion:
h(t) = (1/2)gt + vt + vo
where
h(t) is height
g is gravity
v is initial velocity
t is time
vo is the initial height
.
h(t) = (1/2)(-9.8)t + 5t + 1.3
h(t) = -4.6t + 5t + 1.3
.
set h(t) to zero and solve for t:
0 = -4.6t + 5t + 1.3
applying quadratic formula we get:
t = {-0.217, 1.304}
we can throw out the negative solution leaving:
t = 1.3 seconds
.
Details of quadratic to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.6x%5E2%2B5x%2B1.3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A-4.6%2A1.3=48.92.

Discriminant d=48.92 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+48.92+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+48.92+%29%29%2F2%5C-4.6+=+-0.216769932610683
x%5B2%5D+=+%28-%285%29-sqrt%28+48.92+%29%29%2F2%5C-4.6+=+1.30372645434981

Quadratic expression -4.6x%5E2%2B5x%2B1.3 can be factored:
-4.6x%5E2%2B5x%2B1.3+=+-4.6%28x--0.216769932610683%29%2A%28x-1.30372645434981%29
Again, the answer is: -0.216769932610683, 1.30372645434981. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.6%2Ax%5E2%2B5%2Ax%2B1.3+%29