SOLUTION: Please help with this word problem. If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 80 ft/s, its height h after t s is given by h=-16t^

Question 98246: Please help with this word problem.
If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 80 ft/s, its height h after t s is given by h=-16t^2 + 80t + 5. How long does it take the ball to return to the ground?
thak you very much for your help.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find when it hits the ground, let h=0

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=5

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 possible solutions are:
or

However, since a negative time doesn't make sense, our only solution is
RELATED QUESTIONS
Can you please help me solve this problem? A ball is thrown vertically upward from the... (answered by Alan3354)

Help please! I'm so confused by this problem. Can you explain it step by step? if an... (answered by josmiceli)

If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of... (answered by Alan3354)

A ball is thrown vertically upward from the ground with an initial velocity of 103 feet... (answered by ikleyn)

Word Problem Help A ball is thrown from an initial height of 4 feet with an initial... (answered by MathLover1)

A ball is thrown vertically upward from the ground with an initial velocity of 103 feet... (answered by ikleyn)

Solve. If a ball thrown vertically upward from a height of 5ft, with an initial... (answered by jim_thompson5910)

Help please! I'm so confused by this problem... if an object is thrown vertically... (answered by solver91311,rothauserc)

please help A ball is thrown from an initial height of 5 feet with an initial upward... (answered by ikleyn)