A rope is wound around a hollow cylinder and another is wound around a solid cylinder. The surfaces of the cylinders have some friction. The solid cylinder is 20 times heavier than the hollow cylinder. The ropes are pulled with a constant force of 50 N. Assume that the cylinders acquire an equal angular acceleration. The number of turns on the hollow cylinder is four. If the radius of each cylinder is 14 cm, then what is the length of the rope wound around the solid cylinder?

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An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)