A ski jumper starts from rest from point A at the top of a hill that is a height h1 above point B at the bottom of the hill. The skier and skis have a combined mass of 80 kg. The skier slides down the hill and then up a ramp and is launched into the air at point C that is a height of 10m above the ground. The skier reaches point C traveling at 42m/s.

(a) Calculate the height h1.

(b) Calculate the speed of the skier as the skier reaches point B.

(c) Is the work done by the gravitational force on the skier as the skier slides from point A to point B positive or negative? Justify your answer.

(d) The skier leaves the ramp at point C traveling at an angle of 25° above the horizontal. Calculate the kinetic energy of the skier at the highest point in the skier's trajectory.

(e)

i. Calculate the horizontal distance from the point directly below CC to where the skier lands.

ii. If the angle is increased to 35°, will the new horizontal distance traveled by the skier be greater than, less than, or equal to the answer from part (e)(i)? Justify your answer.

(f) After landing, the skier slides along horizontal ground before coming to a stop. The skier’s initial speed on the ground is the horizontal component of the skier’s velocity when the skier left the ramp. The average coefficient of friction μ is given as a function of the distance x moved by the skier by the equation μ=0.20x. Calculate the distance the skier moves between landing and coming to a stop.