SOLUTION: A rock is tossed straight up with initial velocity of 10 feet per second from atop a balcony 30 ft above the ground. The height of the rock is given by the equation h(t) = -16t^2 +

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Question 1093126: A rock is tossed straight up with initial velocity of 10 feet per second from atop a balcony 30 ft above the ground. The height of the rock is given by the equation h(t) = -16t^2 + 10t + 30 at a time t seconds after the rock was tossed. How many seconds pass before the rock is 20 feet above ground?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since the rock is tossed from a height above
20 ft, then the rock will be falling at 20 ft
-----------------------------------------
+h%28t%29+=+-16t%5E2+%2B+10t+%2B+30+
+20+=+-16t%5E2+%2B+10t+%2B+30+
+-16t%5E2+%2B+10t+%2B+10+=+0+
+-8t%5E2+%2B+5t+%2B+5+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-8+
+b+=+5+
+c+=+5+
+t+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A%28-8%29%2A5+%29%29%2F%282%2A%28-8%29%29+
+t+=+%28-5+-+sqrt%28+25+-%28+-160+%29+%29+%29+%2F+%28-16%29+
+t+=+%28+-5+-+sqrt%28+185+%29+%29+%2F+%28-16%29+
+t+=+%28+-5+-+13.601+%29+%2F+%28-16%29+
+t+=+18.601%2F16+
+t+=+1.163+ sec
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check answer:
here's the plot:
+graph%28+400%2C400%2C+-1%2C3%2C+-5%2C40%2C+-16x%5E2+%2B+10x+%2B+30+%29+
Looks about right