Sisyphus, as the Greek myth goes, was tasked by Zeus aspunishment for his trickery to push a giant boulder up a steep hillin Hades, the top of the hill always just out of reach. Supposethat the angle this hill makes with the level floor is 37.0°, andSisyphus and the boulder have a mass of 121 kg and 637 kg,respectively.

a) During one journey up the hill, Sisyphus tires and brieflylets go of the boulder. To his shock, the boulder stays in placewhere he left it. What is the coefficient of static frictionbetween the boulder and the hill?

b) Zeus, angered to see Sisyphus resting, magically increasesthe slope of the hill to 53.0° so that the boulder begins to rollback down the hill. Sisyphus catches the boulder, and both begin toslide down the hill together. If the coefficient of kineticfriction between Sisyphus's feet and the hill is only 88% of thatbetween the boulder and the hill, and they begin sliding downwardswith an acceleration of 4.5 m/s², what is thecoefficient of kinetic friction between the boulder and thehill?