A40 kg-skier starts at the top of a 12-metter high slope. at the bottom she is travling 10 m/s. how much energy dose she lose to friction

Potential energy at the top = (mass) x (gravity) x (height)

                                           = (40 kg) x (9.8 m/s²) x (12 m)

                                           =            4,704 Joules

Kinetic energy at the bottom = 1/2 (mass) x (speed)²

                                              =  1/2 (40 kg) x (10 m/s)²

                                              =        2,000 Joules .

Energy lost between the top and the bottom
  
                                   (4,704 joules) - (2,000 joules)

                               =            2,704 Joules

The objects are acted upon by only one force. gravity. mass times the acceleration of gravity (-9.81meters/second squared).