SOLUTION: A ball is thrown upward from a 100-foot tall building with an initial velocity of 14 feet per second. Its height s(t) is given by the function s(t)=-16t^2 + 14t +100. Find the inte

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A ball is thrown upward from a 100-foot tall building with an initial velocity of 14 feet per second. Its height s(t) is given by the function s(t)=-16t^2 + 14t +100. Find the inte      Log On


   

Question 1099358: A ball is thrown upward from a 100-foot tall building with an initial velocity of 14 feet per second. Its height s(t) is given by the function s(t)=-16t^2 + 14t +100. Find the interval of time for which the ball is greater than 103 feet.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+s%28t%29+%3E=+103+
+-16t%5E2+%2B+14t+%2B+100+%3E+103+
+-16t%5E2+%2B+14t+-+3+%3E+0+
Use quadratic equation
+t+=+%28+-b+%2B-sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282a%29+
+a+=+-16+
+b+=+14+
+c+=+-3+
------------------
+t+=+%28+-14+%2B-sqrt%28+14%5E2+-+4%2A%28-16%29%2A%28-3%29+%29+%29%2F+%28-32%29+
+t+=+%28+-14+%2B-sqrt%28+196+-+192+%29+%29+%2F+%28-32%29+
+t+=+%28+-14+%2B-sqrt%28+4+%29+%29%2F+%28-32%29+
+t+=+%28+-14+%2B+2+%29+%2F+%28-32%29+
+t+=+3%2F8+
and
+t+=+%28+-14+-+2+%29+%2F+%28-32%29+
+t+=+1%2F2+
-----------------
The ball is higher than 103 ft during the
time interval +.375+%3C+t+%3C+.5+ sec
---------------------------------------
check:
Here's the plot:
+graph%28+400%2C400%2C+-3%2C+3%2C+-15%2C+120%2C+-16x%5E2+%2B+14x+%2B+100+%29+