A water skier lets go of the tow rope upon leaving the end of a jump ramp at a speed of 14.9 m/s. As the drawing indicates, the skier has a speed of 10.9 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.
Drawing? Not here. his angle of launch is important.
I can't manage to add the drawing on this website. But there is no angle on the drawing anyways..
To determine the skier's height above the top of the ramp at the highest point, we can use the principle of conservation of energy. At the highest point, the skier will have maximum potential energy and zero kinetic energy.
First, let's find the initial kinetic energy (KE_initial) of the skier as they leave the end of the jump ramp. We can use the formula:
KE_initial = (1/2) * m * v_initial^2
where m is the mass of the skier and v_initial is the initial velocity of the skier.
Next, let's find the final kinetic energy (KE_final) of the skier at the highest point of the jump. Since the skier has a speed of 10.9 m/s at this point, we can calculate:
KE_final = (1/2) * m * v_final^2
where v_final is the final velocity of the skier.
Since the skier is at the highest point and has zero kinetic energy, we have:
KE_final = 0
Now, let's find the potential energy (PE) of the skier at the highest point using the formula:
PE = m * g * h
where m is the mass of the skier, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above the top of the ramp.
According to the principle of conservation of energy, the initial kinetic energy of the skier will be equal to the sum of the final kinetic energy and the potential energy:
KE_initial = KE_final + PE
Substituting the equations, we have:
(1/2) * m * v_initial^2 = 0 + m * g * h
Simplifying the equation, we get:
v_initial^2 = 2 * g * h
Now we can solve for h, the height above the top of the ramp:
h = v_initial^2 / (2 * g)
Plugging in the given values, we have:
h = (14.9 m/s)^2 / (2 * 9.8 m/s^2)
h = 111.0408163265306 m
Therefore, the skier's height above the top of the ramp at the highest point is approximately 111.04 meters.