Answer:
25 m/s * √(1.5 m/<em>g</em>) ≈ 9.78 m
Explanation:
When effects of air resistance is neglected, the motion can be modeled as
<em>x</em>(<em>t</em>) = 25 m/s * <em>t</em>
<em>y</em>(<em>t</em>) = 1.5 m - <em>g</em> * <em>t</em>²
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 <em>x</em> value is the horizontal travel we’re interested in. Time <em>t</em> begins at the exit of the slide by this rider. <em>g</em> is the gravitational acceleration.
At the time when the rider hits water, we know <em>y</em> = 0.
0 = 1.5 m - <em>g</em> * <em>t</em>² ⇔ <em>t</em> = ±√(1.5 m/<em>g</em>)
Since we are only interested in the non-negative (not past) time range, it’s <em>t</em> = √(1.5 m/<em>g</em>)
The horizontal travel is thus:
x(√(1.5 m/<em>g</em>)) = 25 m/s * √(1.5 m/<em>g</em>) ≈ 25 * √(1.5/9.81) m ≈ 9.78 m