Water Slide Mechanical Energy Problem

[StormPix]

Homework Statement

A 58.5 kg child slides down a water slide with a velocity of 1.2 m/sec at the top. At the bottom of the slide, she is moving horizontally, y=1.5 meters above the water. She splashes into the water d=2 meters to the left of the bottom of the slide.
1) Assuming potential energy to be zero at the water level, what is the mechanical energy of the child at the top of the slide?
a) MEo=

b) Find h

Homework Equations

KE = .5*m*v^2
Wg = mgh
PE = Wc
Yf = Yo + Vo*t + .5*g*t^2
ΔKE = ΔPE
Vf = Vo + a*t

The Attempt at a Solution

So, this is what I tried, and it turned out to not be correct. Maybe I made a mistake somewhere and if so would someone be kind enough to point it out/ help me figure out the correct way to solve this. Thank you.

So I started with knowing there was some initial KE:

KE_t = .5 * 58.5 * (1.2)^2 = 42.12 J

I knew also that at the bottom there is:

KE^b = .5 * 58.5 * v^2 = 29.25 * v^2

I knew from the problem that at the bottom of the slide, the girl is not moving in the Y direction, thus I can assume a standard 2-D kinematic type of problem to solve for V

1.5 = .5 * 9.81 * t^2
t^2 = 3 / 9.81
t = .55 sec

V = 2m / .55sec = 3.64 m/s

I then knew the KE at the bottom when the girl hit the water to be

KE = 29.25(3.64)^2 = 386.78 J

From E_i = E_f I said that the ME_o was 386.78 J... which as it turned out, was not correct.

I stopped here because without knowing the ME_o I could not get h.

 

[TSny]

Hi, StormPix. Welcome to PF!

Looks like you assumed that the speed of 3.64 m/s is the speed of the child when she hits the water. But, actually that's the speed somewhere else. How much potential energy of gravity is there at the point where the speed is 3.64 m/s? (I get 3.61 m/s rather than 3.64 m/s. I don't know if round off error will be important here.)

 

[Simon Bridge]

Check:
* Definition of "mechanical energy".
* Where do you need to calculate the mechanical energy at?