SOLUTION: Solving a science application. Suppose that a ball is thrown upward with an initial velocity of 80 ft/s. (the initial velocity is the speed with which the ball leaves the throwers

Question 119148: Solving a science application. Suppose that a ball is thrown upward with an initial velocity of 80 ft/s. (the initial velocity is the speed with which the ball leaves the throwers hand. The spped will then decrease as the ball rises.) If the ball is released at a height of 77ft, the height equation may be written as follows: h= -16t^2+80t+5, round to the nearest hundredth of a second
77= -16t^2+80t+5
this is all i got, now I am lost, can someone please help me, thank you
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Do you want to solve for t?

Start with the given equation

Subtract 77 from both sides.

Combine like terms

Let's use the quadratic formula to solve for t:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-16, b=80, and c=-72

Square 80 to get 6400

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

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

So when the time is or the ball is at a height of 77 ft.

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