SOLUTION: the height of a model rocket can be measure by the function H(t)=720t-16t^2, where t is time measured in seconds, and H is measured in feet. how long does it take the rocket to rea

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Question 615575: the height of a model rocket can be measure by the function H(t)=720t-16t^2, where t is time measured in seconds, and H is measured in feet. how long does it take the rocket to reach its highest point, and how high does it get
Answer by josmiceli(9661) About Me  (Show Source):
You can put this solution on YOUR website!
++H%28t%29=720t-16t%5E2+
Find 2 points where the height of the rocket is zero
One point is at (0,0) because
++H%28t%29=720%2A0-16%2A0%5E2+
+H%280%29+=+0+
Now set +H%28t%29+=+0+
+0+=+720t+-+16t%5E2+
+0+=+t%2A%28+720+-+16t%29+
This is true if +t+=+0+ or if
+720+-+16t+=+0+
+16t+=+720+
+t+=+45+
So, the 2nd point is at (45,0)
The midpoint of this parabola is at +%28+0+%2B+45+%29+%2F+2+=+22.5+ sec
The find the height at this time,
+H%2822.5%29+=+720%2A22.5+-+16%2A22.5%5E2+
+H%2822.5%29+=+16200+-+8100+
+H%28+22.5%29+=+8100+
The maximum height is 8,100 ft
Here's the plot where height is in hundreds of feet
+graph%28+400%2C+400%2C+-5%2C+50%2C+-15%2C+100%2C+7.2x+-+.16x%5E2+%29+