SOLUTION: Robin Hood shoots an arrow from a window in Nottingham Castle to escape the evil Prince John. The relation h = -t2 + 4t + 21 models the height of the arrow as it makes its way to
Question 1167804: Robin Hood shoots an arrow from a window in Nottingham Castle to escape the evil Prince John. The relation h = -t2 + 4t + 21 models the height of the arrow as it makes its way to a 9 m high tree across the moat. t is time in seconds, h is height in metres.
How high is the window?
What is the maximum height of the arrow?
If the arrow hits the top of the tree on its way down, how long does it take the arrow to reach the tree?
You can put this solution on YOUR website! h=-t^2+4t+21
The window is 21 m high (the constant in the formula)
the maximum is at t=-b/2a or -4/-2 or at 2 seconds
h(2)=-4+8+21=25 m maximum
9=-t^2+4t+21
t^2-4t-12=0
(t-6)(t+2)=0
t=6 and -2, which can be ignored.
at 6 seconds, h will be 9 meters, so the answer is 6 seconds
