SOLUTION: jessie kicked a soccer ball into the air with an initial upward velocity of 40 feet per second. The hieght (h) in feet of the ball above the ground can be modeled by h=-16t2+40t,wh

Question 118286: jessie kicked a soccer ball into the air with an initial upward velocity of 40 feet per second. The hieght (h) in feet of the ball above the ground can be modeled by h=-16t2+40t,where t is the time in seconds after jessie kicked the ball. find the time it takes the ball to reach 25 feet above the grond.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since we're finding the time it takes for the ball to reach 25 feet, this means h is 25

Start with the given equation

Plug in

Add to both sides. Subtract from both sides.

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=16, b=-40, and c=25

Negate -40 to get 40

Square -40 to get 1600 (note: remember when you square -40, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 16 to get 32

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our only solution is:

(which is in decimal form)

So at 1.25 seconds, the ball is 25 feet high.

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