To find the maximum height, we need to find the vertex of the parabolic equation h=−4.9t2+58.8t. The vertex occurs at t=−b/2a, where a=−4.9 and b=58.8.
t=−58.8/(2(-4.9))=6
So the water reaches its maximum height at 6 seconds.
To find the maximum height, we plug in t=6 into the equation:
h=−4.9(6)2+58.8(6)= 176.4 meters
Therefore, the maximum height of the water is 176.4 meters.
To find the amount of time it takes for the water to reach the ground, we need to find when h=0. Set h=0 in the equation:
0=−4.9t2+58.8t
0=t(−4.9t+58.8)
t=0 or t=12
Since t=0 is the starting point, we ignore that solution. Therefore, the water reaches the ground after 12 seconds.
So the amount of time it takes for the water to reach the ground is 12 seconds.
The path of water sprayed from a fountain is modeled by h=−4.9t2+58.8t,
where h is the height of the water in meters after t seconds. Determine the maximum height of the water and the amount of time it takes the water to reach the ground.
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