A child starts from rest and slides without friction from a height of h = 5.1 m

Question

A child starts from rest and slides without friction from a height of h = 5.1 m along a slide next to a pool (see figure). She is launched from a height of 0.8 m (ignore the h/5 in the figure) at an angle of 28° into the air over the pool.

What is her maximum height above the water after leaving the slide? Hint: it is possible to do this without doing projectile motion, even desirable as we are trying to learn conservation of energy; this problem does require you to use conservation of energy more than once.

Explanation / Answer

Let's take the location of PE = 0 to be at the end of the slide.
In falling from 5.1m to 0.8m, the person has converted
M * 9.8m/s² * 4.3m = 42.14M m²/s²

v = 2gh = 9.18 m/s

This has vertical component Vv = 9.18m/s * sin28º = 4.30 m/s
which gets converted back into PE (while the horizontal component stays constant).
h = v² / 2g = 4.30² / 19.6 = 0.94 m
above the end of the slide, or 3.36 m above the water.

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