A water skier lets go of the tow rope upon leaving the end of a jump ramp at a speed of 17.9 m/s. As the drawing indicates, the skier has a speed of 11.1 m/s at the highest point of the jump. Ignoring air resistance, determine the skier's height H above the top of the ramp at the highest point.

Question

A water skier lets go of the tow rope upon leaving the end of a jump ramp at a speed of 17.9 m/s. As the drawing indicates, the skier has a speed of 11.1 m/s at the highest point of the jump. Ignoring air resistance, determine the skier's height H above the top of the ramp at the highest point.
 m

drwls · Accepted Answer

At the highest point of the jump, the velocity will have only a horizontal component: 11.1 m/s. Since that component is constant, the vertical component when leaving the ramp was

sqrt[(17.9)^2 - (11.1)^2] = 14.0 m/s

The initial vertical velocity component, Vyo, can be used to calculate the maximum height H. The time that the jumper spends going up is
T = Vy,0/g. The average velocity while going up is Vy,o/2. H is the product of those two numbers.