Question

The water reaches a max height when the horizontal distance from the firefighter to the building is approximately __m. Round to 1 decimal place

Answer 1

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,

$x = \frac{-0.563}{2 X -0.026} \\\\x = \frac{0.563}{0.052}\\ \\x = 10.83m$

Therefore, horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m