SOLUTION: if an orange is tossed upward from a height of 13 feet at an initial velocity of 18 feet per second, then its height h after t seconds is given by the function h(t)= -16t^2+18t+13,

Question 904309: if an orange is tossed upward from a height of 13 feet at an initial velocity of 18 feet per second, then its height h after t seconds is given by the function h(t)= -16t^2+18t+13, where h is in feet.
A. How long will the object be in the air before it hits the ground?
b. How long will it take to reach 4 feet?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
A) set h(t) to 0 and solve
0= -16t^2+18t+13

Solved by pluggable solver: Quadratic Formula

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=18, and c=13

Square 18 to get 324

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 solutions are:

or

t = 13/8
B) set h(t) to 4 and solve
4= -16t^2+18t+13
t=3/2

Solved by pluggable solver: Quadratic Formula

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=18, and c=9

Square 18 to get 324

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 solutions are:

or

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