SOLUTION: I need help with this one homework question. A ball is thrown into the air with an initial upward velocity of 60ft/sec. Its height (h) in feet after 1 sec is given by the functio

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Question 284087: I need help with this one homework question.
A ball is thrown into the air with an initial upward velocity of 60ft/sec. Its height (h) in feet after 1 sec is given by the function h=-16t2(2= squared cant make a little 2)+60t +6
a: after how many seconds will the ball hit the ground?
b: what will the height be at if t= 3 seconds
i think for part be the answer is 42 ive plugged in 3 for t and got 42 i have no idea how to get part A
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A ball is thrown into the air with an initial upward velocity of 60ft/sec. Its height (h) in feet after 1 sec is given by the function h=-16t2(2= squared cant make a little 2)+60t +6

Not for 1 second, but at t seconds
------------------------------------
a: after how many seconds will the ball hit the ground?
It hits the ground when h(t) = 0



Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=996 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -0.0974667297574374, 3.84746672975744. Here's your graph:

Use the + value, ~3.847 seconds
--------------------------------
b: what will the height be at if t= 3 seconds
h(3) = -16*9 + 60*3 + 6 = -144 + 180 + 6
h(3) = 42 feet
------------------
i think for part be the answer is 42 ive plugged in 3 for t and got 42 i have no idea how to get part A
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