1. A cyclist starts from rest and freewheels down a hill inclined at arcsin 1/20 to the horizontal. After traveling 80 m the road becomes horizontal and the cyclist travels another 80 m before coming to rest without using his brakes. Given that the combined mass of the cyclist and his machine is 80 kg, model the cyclist and his machine as a single particle and hence find the resistive force, assumed constant throughout the motion.
2. A boy and his skateboard have a mass of 50 kg. He descends a slope inclined at 12(degrees) to the horizontal from rest. At the bottom, the ground becomes horizontal for 10 m before rising at 8(degrees) to the horizontal. The boy travels 30 m up the incline before coming to rest again. He is subject to a constant resistance of 20 N throughout the motion. By modeling the boy and his skateboard as a single particle find the distance the boy traveled down the slope.
3. A book slides down a rough desk lid which is inclined at 30(degrees) to the horizontal and falls to the ground which is 0.8 m below the edge of the lid. The coefficient of friction between the book and the lid is 1/4. Given that the book starts from rest 0.4 m from the bottom of the lid which is hinged is at the edge of the desk, find the speed with which the book hits the floor.
4. A rough plane is inclined at arcsin 3/5 to the horizontal. A package of mass 40 kg is released from rest and travels 15 m while increasing speed to 12 m/s. Find, using energy considerations, the coefficient of friction between the package and the plane.
Im revising for my Mechanics 2 A2 Level exam so ill be really grateful.... Thankyou....