Agiant challenges a dwarf to a competition. each has to move a block of mass m along a horizontal surface through a distance d, starting from rest. the one whose block has the largest kinetic energy at the end will be the winner. the giant is strong. he will push his block with a constant pushing force of magnitude p, directed at an angle θ below the horizontal. he is also lazy and leaves the bottom of his block rough so that there will be a coefficient of kinetic friction μ between his block and the surface. the dwarf is smart. he will launch his block from a spring of spring constant k that is compressed a distance l. he also makes the bottom of his block smooth so that there is no kinetic friction between block and surface. the giant graciously lets the dwarf decide the distance of the race. use the work-kinetic energy theorem to derive an expression for the maximum distance d for which the dwarf can be sure to win the competition.