SOLUTION: Suppose you throw an egg vertically into the air from a height of 6 feet above the ground at an initial velocity of 46 feet per second. h=-16t^2+46t+6 Find when the egg hit t

Algebra ->  Radicals -> SOLUTION: Suppose you throw an egg vertically into the air from a height of 6 feet above the ground at an initial velocity of 46 feet per second. h=-16t^2+46t+6 Find when the egg hit t      Log On


   

Question 539258: Suppose you throw an egg vertically into the air from a height of 6 feet above the ground at an initial velocity of 46 feet per second.
h=-16t^2+46t+6 Find when the egg hit the ground.
time in seconds / height of egg
0 / ?
.5 / ?
1 / ?
1.5 / ?
2 / ?
2.5 / ?
3 / ?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose you throw an egg vertically into the air from a height of 6 feet above the ground at an initial velocity of 46 feet per second.
h=-16t^2+46t+6 Find when the egg hit the ground.
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It hits the ground when h = 0.
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h=-16t^2+46t+6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B46x%2B6+=+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=%2846%29%5E2-4%2A-16%2A6=2500.

Discriminant d=2500 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-46%2B-sqrt%28+2500+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2846%29%2Bsqrt%28+2500+%29%29%2F2%5C-16+=+-0.125
x%5B2%5D+=+%28-%2846%29-sqrt%28+2500+%29%29%2F2%5C-16+=+3

Quadratic expression -16x%5E2%2B46x%2B6 can be factored:
-16x%5E2%2B46x%2B6+=+%28x--0.125%29%2A%28x-3%29
Again, the answer is: -0.125, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B46%2Ax%2B6+%29

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t = x
Ignore the negative solution.
t = 3 seconds