SOLUTION: A ball is thrown into the air. The path of the ball is given by the quadratic formula h (t)= -4.9t^2+6.1t, where t is measured in seconds and h (t) in metres. How can i decide with

Question 1023285: A ball is thrown into the air. The path of the ball is given by the quadratic formula h (t)= -4.9t^2+6.1t, where t is measured in seconds and h (t) in metres. How can i decide without completely solving this problem whether or not the ball will ever reach a height of 2 metres above the ground?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
-4.9t^2 means that ball follows a parabolic path that curves downward
:
The first derivative is
:
-9.8t +6.1
:
Now set first derivative = 0
:
-9.8t +6.1 = 0
:
-9.8t = -6.1
:
t is approx 0.6 seconds
:
The ball reaches max height at 0.6 seconds
:
h(0.6) = -4.9 (0.6)^2 +6.1 (0.6)
:
max height reached is 1.9 meters
:
*********************************************
The ball does not reach a height of 2 meters
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