SOLUTION: A diver dives into a swimming pool from the diving board. His height in feet is given by y(t) = −16t2 + 32t + 20, where t is the time in seconds. The horizontal distance in f

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A diver dives into a swimming pool from the diving board. His height in feet is given by y(t) = −16t2 + 32t + 20, where t is the time in seconds. The horizontal distance in f      Log On


   

Question 1030625: A diver dives into a swimming pool from the diving board. His height in feet is given by y(t) = −16t2 + 32t + 20, where t is the time in seconds. The horizontal distance in feet of the diver from the diving board is given by x(t) = 2t. What horizontal distance will the diver travel before he hits the water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Equation for vertical height, +y+
+y%28t%29+=+-16t%5E2+%2B+32t+%2B+20+
It looks like the diving board is +20+ ft
above the water, because when +t=0+
+y%280%29+=+-16%2A0%5E2+%2B+32%2A0+%2B+20+
--------------------------------
You want to know what +t+ is when
+y%28t%29+=+0+ ( the water level )
--------------------------------
+0+=+-16t%5E2+%2B+32t+%2B+20+
+-16t%5E2+%2B+32t+=+-20+
+t%5E2+-+2t+=+5%2F4+
Complete the square
+t%5E2+-+2t+%2B+%28-2%2F2%29%5E2+=+5%2F4+%2B+%28-2%2F2%29%5E2+
+t%5E2+-+2t+%2B+1+=+5%2F4+%2B+4%2F4+
+%28+t+-+1+%29%5E2+=+9%2F4+
+%28+t+-+1+%29%5E2++=+%283%2F2%29%5E2+
+t+-+1+=+3%2F2+
+t+=+5%2F2+
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Equation for horizontal distance:
+x%28t%29+=+2t+
+x%28+5%2F2+%29+=+2%2A%28+5%2F2+%29+
+x%28+5%2F2+%29+=+5+ ft
The diver travels 5 ft horizontally as he hits the water
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check:
+y%28t%29+=+-16t%5E2+%2B+32t+%2B+20+
+y%285%2F2%29+=+-16%2A%285%2F2%29%5E2+%2B+32%2A%285%2F2%29+%2B+20+
+y%285%2F2%29+=+-16%2A%28+25%2F4+%29+%2B+160%2F2+%2B+20+
+y%285%2F2%29+=+-100+%2B+80+%2B+20+
+y%285%2F2%29+=+0+ ( water level )
OK