Astudent, starting from rest, slides down a water slide. on the way down, a kinetic frictional force (a nonconservative force) acts on her. the student has a mass of 77 kg, and the height of the water slide is 12.0 m. if the kinetic frictional force does -6.7 × 103 j of work, how fast is the student going at the bottom of the slide?

7.8 m/s

Explanation:

At the top of the slide, the mechanical energy of the student is just gravitational potential energy, given by:

where m=77 kg is the mass of the student, g=9.8 m/s^2 is the gravitational acceleration, h=12.0 m is the height of the slide. Substituting,

While she slides down, the frictional force does

on her. So, the final mechanical energy of the student at the bottom of the slide is

And this energy is just equal to the final kinetic energy of the student, since its potential energy is just zero (at the bottom of the slide, h=0):

where v is the final speed of the student. Solving for v,