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