You are at the park; it has just finished snowing. you are trying to pull your kid sister on a sled as fast as possible. the sled and your sister together have a total mass m. the sled is old, so there is some small, constant coefficient of kinetic friction uk between the sled bottom and the snow. (remember that we model kinetic friction as being simply proportional to the magnitude of the normal force |n|, that is f friction = ukn.) a) [6 pts] you can pull at any angle you want, with some given, fixed arm-force farml.

a. at what angle should you pull to accelerate your sister and the sled forward as fast as possible?

b) [5 pts) after you find the angle, figure out a formula for this maximum forward acceleration for sister and sled. as in part a), your answer should just be in terms of the given constants.

c) [3 pts) explicitly check both your answers in part a) and part b) by considering units.

d) [3 pts) examine the limit of u k +0. does the result make sense? briefly explain.

e) [3 pts) examine the limit of very large uk, that is pk +00. explain your result.