What's Wrong with My Conservation of Energy Calculation for a Skier?

[vroman]

Here's a problem involving conservation of energy. My answer is wrong, but I can't figure out why. I would be extremely grateful for some help

A skier (m=59.00 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally. If h, the height of the end of the ski jump, is 3.40m and D, the distance from the end of the jump to his landing point, is 10.90 m, find H, the height of the top of the ski jump.

The answer I'm getting is 55.63m

Step 1: To begin, I calculated the horizontal velocity of the skier at the end of the jump.
v^2=2gm
v^2=2(9.8m/s^2)(59kg)
v=34.01m/s
Step 2: Then, I calculated the time, using Newton's Kinematic Equations for Projectile Motion.
y=y0+vy0t-1/2gt^2
-3.4=0+0-1/2(9.8)t^2
t=.833s
Step 3: I calculated the x and y components of the velocity of the skier when he lands on the ground.
vx=vx0
vx=34.01m/s
vy=vy0-gt
vy=0-9.8(.833)
vy=-8.16m/s
Step 4: I calculated the velocity of the skier when he lands by using the Pythagorean Theorum.
v=33.02m/s
Step 5: I used the equation for conservation of energy to determine the height at the top of the ski jump.
KE1+PE1=KE2+PE2
KE1=0
PE1=mgy1=(59kg)(9.8m/s^2)(y1)=578y1
KE2=1/2mv^2=1/2(59kg)(33.02m/s)^2= 32164.45J
PE2=mgy2=(59kg)(9.8m/s)(0)=0
0+578.2y1=32164.45J+0
y1=55.63m

 

[WhirlwindMonk]

I'll bet your problem is that your first equation is wrong. The units don't match. you have m^2/s^2=kg*m/s^2. The equation you want is v-final^2=v-initial^2+2gh, and I also believe you mean vertical velocity, not horizontal in your first step.

 

[whozum]

That first equation isn't right, if you're using energy analysis, that m should be an h.

This is a really unclear problem. If he takes off horizontally, his max height is 3.40m