Physics q....don't know where to begin with both distances?

Question

An extreme skier, starting from rest, coasts down a mountain that makes an angle 25.0° with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.200. She coasts for a distance of 10.2 m before coming to the edge of a cliff. Without slowing down, she skis off the cliff and lands downhill at a point whose vertical distance is 4.10 m below the edge. How fast is she going just before she lands?

Answer 1

a = 9.81(sin25 - 0.2 cos25)
v = √(2*9.81(sin25 - 0.2 cos25)*10.2) at take-off
vyi = (√(2*9.81(sin25 - 0.2 cos25)*10.2))sin25
vxi = (√(2*9.81(sin25 - 0.2 cos25)*10.2))cos25
vyf^2 - vyi^2 = 2*4.1*9.81
vyf^2 = 2*4.1*9.81 + 2*9.81(sin25 - 0.2 cos25)*10.2)sin^2(25)
vf^2 = 2*4.1*9.81 + 2*9.81(sin25 - 0.2 cos25)*10.2)sin^2(25) + (2*9.81(sin25 - 0.2 cos25)*10.2))cos^2(25)
vf^2 = 2*4.1*9.81 + 2*9.81(sin25 - 0.2 cos25)*10.2)
vf^2 = 2*9.81(4.1 + 10.2(sin25 - 0.2 cos25))
vf^2 = 2*9.81(4.1 + 10.2(0.422618262 - 0.181261557))
vf^2 = 2*9.81(4.1 + 10.2(0.241356704))
vf^2 = 2*9.81(4.1 + 2.46183838)
vf^2 = 2*9.81(6.56183838)
vf^2 = 128.743269
vf = 11.347 m/s

Answer 2

Her acceleration down the slope is the component of gravity down the slope minus friction:

a = mg sin 25 - 0.2 mg

Then use v^2 = u^2 + 2as to find the speed as she leaves the slope. Resolve into horizonal and vertical components. Use the horizontal component and the 4.10m distance to calculate her time in the air. Then use v = u + gt to find the vertical component of the velocity just before she lands. Finally combine the horizontal (which hasn't changed) and vertical components of the velocity to find the magnitude.

Answer 3

Before I go doing the math, please complete the question. Which direction? Forward or downward. As she skies down the slope she gains forward velocity. When she goes over the cliff she no longer accelerates forward but downward due to gravity. So you have two velocities to contend with. I'll get back to you after work tonight but I bet somebody will just answer both questions.