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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (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
h%28t%29+=+-16t%5E2+%2B+60t+%2B+6
Not for 1 second, but at t seconds
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a: after how many seconds will the ball hit the ground?
It hits the ground when h(t) = 0
h%28t%29+=+-16t%5E2+%2B+60t+%2B+6
0+=+-16t%5E2+%2B+60t+%2B+6
-8t%5E2+%2B+30t+%2B+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -8x%5E2%2B30x%2B3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2830%29%5E2-4%2A-8%2A3=996.

Discriminant d=996 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+996+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+996+%29%29%2F2%5C-8+=+-0.0974667297574374
x%5B2%5D+=+%28-%2830%29-sqrt%28+996+%29%29%2F2%5C-8+=+3.84746672975744

Quadratic expression -8x%5E2%2B30x%2B3 can be factored:
-8x%5E2%2B30x%2B3+=+%28x--0.0974667297574374%29%2A%28x-3.84746672975744%29
Again, the answer is: -0.0974667297574374, 3.84746672975744. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B30%2Ax%2B3+%29

Use the + value, ~3.847 seconds
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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
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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