A water-skier lets go of the tow rope upon leaving the end of a jump ramp at a speed of v1 = 14.7 m/s. the skier has a speed of v2 = 12.7 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.
To determine the skier's height above the top of the ramp at the highest point, we can use the conservation of energy principle.
We know that at the highest point of the jump, the skier's velocity is v2 = 12.7 m/s. Since air resistance is ignored, we can assume that the only forces acting on the skier are gravity and the normal force.
The conservation of energy principle states that the total mechanical energy (the sum of kinetic energy and potential energy) remains constant in the absence of external forces.
At the highest point of the jump, all of the skier's initial kinetic energy will be converted into potential energy. Therefore, we can equate the initial kinetic energy to the potential energy.
The initial kinetic energy can be calculated using the formula:
KE = (1/2) * m * v1^2
where m is the mass of the skier and v1 is the initial velocity of the skier.
The potential energy at the highest point can be calculated using the formula:
PE = m * g * h
where m is the mass of the skier, g is the acceleration due to gravity, and h is the height above the top of the ramp.
Since the total mechanical energy remains constant, we can equate the initial kinetic energy to the potential energy:
(1/2) * m * v1^2 = m * g * h
We can now solve for h:
h = (1/2) * (v1^2) / g
Substituting the given values:
v1 = 14.7 m/s
g = 9.8 m/s^2
h = (1/2) * (14.7^2) / 9.8
h = (1/2) * 216.09 / 9.8
h ≈ 10.964 meters
Therefore, the skier's height above the top of the ramp at the highest point is approximately 10.964 meters.