SOLUTION: an arrow is shot into the air from a building that is 32ft high. the height of the arrow after t seconds is given by the formula h(t)=-16t^2+48t+32=0 when will the arrow hit the g

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Question 751433: an arrow is shot into the air from a building that is 32ft high. the height of the arrow after t seconds is given by the formula h(t)=-16t^2+48t+32=0
when will the arrow hit the ground?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solve -16t%5E2%2B48t%2B32=0 for t

Use the quadratic formula to solve for t

t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

t+=+%28-%2848%29%2B-sqrt%28%2848%29%5E2-4%28-16%29%2832%29%29%29%2F%282%28-16%29%29 Plug in a+=+-16, b+=+48, c+=+32

t+=+%28-48%2B-sqrt%282304-%28-2048%29%29%29%2F%28-32%29

t+=+%28-48%2B-sqrt%282304%2B2048%29%29%2F%28-32%29

t+=+%28-48%2B-sqrt%284352%29%29%2F%28-32%29

t+=+%28-48%2Bsqrt%284352%29%29%2F%28-32%29 or t+=+%28-48-sqrt%284352%29%29%2F%28-32%29

t+=+%28-48%2B16%2Asqrt%2817%29%29%2F%28-32%29 or t+=+%28-48-16%2Asqrt%2817%29%29%2F%28-32%29

t+=+%283-sqrt%2817%29%29%2F2 or t+=+%283%2Bsqrt%2817%29%29%2F2

t+=+-0.561553 or t+=+3.561553

Ignore the negative solution (since a negative time doesn't make sense)

So the only solution is approximately t+=+3.561553

This means it will take approximately 3.561553 seconds for it to hit the ground.