SOLUTION: An object is thrown upward from the top of a 96-foot building with an initial velocity of 80 per second. The height h of the object after t is given by the quadratic equation h=16t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: An object is thrown upward from the top of a 96-foot building with an initial velocity of 80 per second. The height h of the object after t is given by the quadratic equation h=16t      Log On


   

Question 731857: An object is thrown upward from the top of a 96-foot building with an initial velocity of 80 per second. The height h of the object after t is given by the quadratic equation h=16t+80t+96
When will the object hit the ground at when the time is how many seconds?
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation should be:
+h%28t%29+=+-16t%5E2+%2B+80t+%2B+96+
The object will hit the ground when
+h%28t%29+=+0+ , so
+0+=+-16t%5E2+%2B+80t+%2B+96+
Divide both sides by +16+
+0+=+-t%5E2+%2B+5t+%2B+6+
Using the quadratic equation:
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+5+
+c+=+6+
+t+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A%28-1%29%2A6+%29%29+%2F+%282%2A%28-1%29%29+
+t+=+%28-5+%2B-+sqrt%28+25+%2B+24+%29%29+%2F+%28-2%29+
+t+=+%28-5+%2B-+sqrt%28+49+%29%29+%2F+%28-2%29+
+t+=+%28+-5+-+7+%29+%2F+%28-2%29+ ( can't use the (+) square root, gives negative t )
+t+=+6+
The object hits the ground in 6 sec
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+7%2C+-10%2C+220%2C+-16x%5E2+%2B+80x+%2B+96+%29+

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An object is thrown upward from the top of a 96-foot building with an initial velocity of 80 per second. The height h of the object after t is given by the quadratic equation h=16t+80t+96
When will the object hit the ground at when the time is how many seconds?
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Using your equation, it will never hit the ground.
Use h(t) = -16t^2 + 80t + 96
Notice the first term is negative, and it's t^2.
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Use h(t) = -16t^2 + 80t + 96
It hits the ground when h(t) = 0
Use h(t) = -16t^2 + 80t + 96 = 0
Solve for t
Ignore the negative value of t.