SOLUTION: This is a vertical motion problem. I need to know what t equals (there should be 2 answers I believe) Problem: 0 = -16t^2 + 8t + 4

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Question 189550: This is a vertical motion problem. I need to know what t equals (there should be 2 answers I believe) Problem: 0 = -16t^2 + 8t + 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

0=-16t%5E2%2B8t%2B4 Start with the given equation.


Notice we have a quadratic equation in the form of at%5E2%2Bbt%2Bc where a=-16, b=8, and c=4


Let's use the quadratic formula to solve for t


t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


t+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%28-16%29%284%29+%29%29%2F%282%28-16%29%29 Plug in a=-16, b=8, and c=4


t+=+%28-8+%2B-+sqrt%28+64-4%28-16%29%284%29+%29%29%2F%282%28-16%29%29 Square 8 to get 64.


t+=+%28-8+%2B-+sqrt%28+64--256+%29%29%2F%282%28-16%29%29 Multiply 4%28-16%29%284%29 to get -256


t+=+%28-8+%2B-+sqrt%28+64%2B256+%29%29%2F%282%28-16%29%29 Rewrite sqrt%2864--256%29 as sqrt%2864%2B256%29


t+=+%28-8+%2B-+sqrt%28+320+%29%29%2F%282%28-16%29%29 Add 64 to 256 to get 320


t+=+%28-8+%2B-+sqrt%28+320+%29%29%2F%28-32%29 Multiply 2 and -16 to get -32.


t+=+%28-8+%2B-+8%2Asqrt%285%29%29%2F%28-32%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


t+=+%28-8%2B8%2Asqrt%285%29%29%2F%28-32%29 or t+=+%28-8-8%2Asqrt%285%29%29%2F%28-32%29 Break up the expression.


t+=+%281-sqrt%285%29%29%2F%284%29 or t+=+%281%2Bsqrt%285%29%29%2F%28-32%29 Reduce


So the answers are t+=+%281-sqrt%285%29%29%2F%284%29 or t+=+%281%2Bsqrt%285%29%29%2F%28-32%29


which approximate to t=-0.309 or t=0.809


Since a negative time doesn't make sense, this means that the only logical solution is t=0.809


So it takes about 0.809 seconds for the object to hit the ground