Simple energy/kinematics problem

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SUMMARY

The problem involves calculating the horizontal distance a person lands from the base of a water slide that is 4.0 m high, with a launch point 1.5 m above the water surface. The correct answer, as per the book, is 4.9 m, while the user initially calculated 3.9 m. The solution requires applying conservation of mechanical energy and kinematics principles to determine the initial velocity and the time of flight. The user clarified the height measurement, confirming that the 4.0 m is the total height from the top of the slide to the water surface.

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I'm not seeing my mistake, but I'm not getting the answer in the back of the book.

Homework Statement


A water slide has a height of 4.0 m. The people coming down the slide shoot out horizontally at the bottom, which is a distance of 1.5 m above the surface of the water in the pool. If a person starts down the slide from rest, neglecting frictional losses, how far from a point directly below the bottom of the slide does the person land?

Homework Equations


Just conservation of mechanical energy, and kinematics.

The Attempt at a Solution


The book gives 4.9 m, but here is my work where I get 3.9 m. I almost hate to ask what I'm doing wrong...
 

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Recheck your calculation for the initial velocity. What's the change in height from the top of the slide to the bottom of the slide?
 
Oh - would the 4.0 m be the distance from the top of the water slide to the pool, or the distance from the top of the water slide to the bottom?

(Ok just answered my own question - thanks)
 

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