SOLUTION: the height h in feet of a ball t seconds after being tossed upwards is given by the function h(t)=84t-16tē a. After hown many seconds will hit the ground? b. What is its maxi

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Question 647609: the height h in feet of a ball t seconds after being tossed upwards is given by the function h(t)=84t-16tē
a. After hown many seconds will hit the ground?
b. What is its maximum height?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+84t+-+16t%5E2+
(a)
It hits the ground when +h+=+0+
There are 2 times when +h+=+0+
The first is at +t+=+0+ when the ball
is thrown upwards.
The second is when the ball actually hits the ground
+h%28t%29+=+0+
+0+=+84t+-+16t%5E2+
+0+=+t%2A%28+84+-+16t+%29+
The ways to make the equation true is
(1) Make +t+=+0+ ( when ball is thrown upward )
(2) Make +84+-+16t+=+0+
+84+-+16t+=+0+
+16t+=+84+
+t+=+5.25+ sec
---------------
(b)
With a parabola ( which it is ) the max or min
occurs midway between the 2 solutions, so
it is at:
+%28+0+%2B+5.25+%29+%2F+2++=+2.625+ sec
Now find +h%28+2.625+%29+
+h%282.625%29+=+84%2A2.625+-+16%2A2.625%5E2+
+h%282.625%29+=+220.5+-+110.25+
+h%282.625%29+=+110.25+ ft
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+6%2C+-10%2C+120%2C+84x+-+16x%5E2+%29+