The horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m
Explanation:
Given:
h(x) = -0.026x² + 0.563x + 3
where,
h(x) is the height of the water
Initial speed, u = 14m/s
angle, θ = 30°
(a)
Horizontal distance = ?
h(x) = ax² + bx + c
the vertex is found at x = -b/2a
where,
x = distance to the maximum height
As compared to the equation given:
a = -0.026
b = 0.563
Thus,
[tex]x = \frac{-0.563}{2 X -0.026} \\\\x = \frac{0.563}{0.052}\\ \\x = 10.83m[/tex]
Therefore, horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m
