Answer:
25 m/s * √(1.5 m/g) ≈ 9.78 m
Explanation:
When effects of air resistance is neglected, the motion can be modeled as
x(t) = 25 m/s * t
y(t) = 1.5 m - g * t²
based on a coordinate system where the x axis is on the water level (modeled as a plane), y axis being parallel to the gravitational force and the point of origin sitting at the point on the water surface directly below the exit of the slide. The x value is the horizontal travel we’re interested in. Time t begins at the exit of the slide by this rider. g is the gravitational acceleration.
At the time when the rider hits water, we know y = 0.
0 = 1.5 m - g * t² ⇔ t = ±√(1.5 m/g)
Since we are only interested in the non-negative (not past) time range, it’s t = √(1.5 m/g)
The horizontal travel is thus:
x(√(1.5 m/g)) = 25 m/s * √(1.5 m/g) ≈ 25 * √(1.5/9.81) m ≈ 9.78 m
