SOLUTION: If an object is given an initial velocity of v0 feet per second from a height of S0 feet, then its height S after t seconds is given by the formula S = -16t2 +v0t + S0. A rock is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: If an object is given an initial velocity of v0 feet per second from a height of S0 feet, then its height S after t seconds is given by the formula S = -16t2 +v0t + S0. A rock is      Log On


   

Question 278774: If an object is given an initial velocity of v0 feet per second from a height of S0 feet, then its height S after t seconds is given by the formula S = -16t2 +v0t + S0. A rock is thrown into the air at 26 feet per second from a height of 13 feet. How long does it take to reach the earth?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
S+=+-16t%5E2+%2Bv0t+%2B+S0
A rock is thrown into the air at 26 feet per second from a height of 13 feet.
So S0 = 13 and V0= 26. The height when it hits the ground is 0
0+=+-16t%5E2+%2B+26t+%2B+13
Use the quadratic equation to solve
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B26x%2B13+=+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=%2826%29%5E2-4%2A-16%2A13=1508.

Discriminant d=1508 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-26%2B-sqrt%28+1508+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2826%29%2Bsqrt%28+1508+%29%29%2F2%5C-16+=+-0.401030489934225
x%5B2%5D+=+%28-%2826%29-sqrt%28+1508+%29%29%2F2%5C-16+=+2.02603048993423

Quadratic expression -16x%5E2%2B26x%2B13 can be factored:
-16x%5E2%2B26x%2B13+=+%28x--0.401030489934225%29%2A%28x-2.02603048993423%29
Again, the answer is: -0.401030489934225, 2.02603048993423. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B26%2Ax%2B13+%29