SOLUTION: Jason jumped off a cliff into the ocean. His height function can be modeled by h(t)= -16t^2+16t+480 How long did it take for Jason to reach his maximum height. What is the highest

Algebra ->  Matrices-and-determiminant -> SOLUTION: Jason jumped off a cliff into the ocean. His height function can be modeled by h(t)= -16t^2+16t+480 How long did it take for Jason to reach his maximum height. What is the highest      Log On


   

Question 703113: Jason jumped off a cliff into the ocean. His height function can be modeled by h(t)= -16t^2+16t+480
How long did it take for Jason to reach his maximum height. What is the highest point he reached. Jason hit the water in how many seconds
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It looks like he jumped up a little bit.
He jumped at +t+=+0+
+h%280%29+=+-16%2A0%5E2+%2B+16%2A0+%2B+480+
+h%280%29+=+480+ ( the height of the cliff )
and
+h%281%29+=+-16%2A1%5E2+%2B+16%2A1+%2B+480+
+h%281%29+=+-16+%2B+16+%2B+480+
+h%281%29++=+480+ ( he's going back down after jumping up )
His peak is at the 1/2 point of the two times
+%28+0+%2B+1+%29+%2F+2+=+1%2F2+
His peak is at +t+=+1%2F2+ sec
--------------------------
That peak is:
+h%281%2F2%29+=+-16%2A%281%2F2%29%5E2+%2B+16%2A%281%2F2%29+%2B+480+
+h%281%2F2%29+=+-4++%2B+8+%2B+480+
+h%281%2F2%29+=+484+ ft
------------------
Jason hit the water when +h+=+0+
+0+=+-16t%5E2+%2B+16t+%2B+480+
+-t%5E2+%2B+t++%2B+30+=+0+
+t%5E2+-+t+-+30+=+0+
+t%5E2+-+t+=+30+
+t%5E2+-+t+%2B+%28-1%2F2%29%5E2+=+30+%2B+%28-1%2F2%29%5E2+
+t%5E2+-+t++%2B+1%2F4+=+30+%2B+1%2F4+
+%28+t+-+1%2F2+%29%5E2+=+121%2F4+
Take the square root of both sides
+t+-+1%2F2+=+11%2F2+
+t+=+1%2F2+%2B+11%2F2+
+t+=+12%2F2+
+t+=+6+
He hit the water in 6 sec
here's the plot:
+graph%28+400%2C+400%2C+-1%2C+7%2C+-50%2C+550%2C+-16x%5E2+%2B+16x+%2B+480+%29+