The Horizontal Boom Supporting the Sign Is of Uniform Construction

A ladder is extended to a length of 8 m. It rests against a smooth frictionless vertical wall at an angle of 55 degrees to the horizontal. The ladder has a mass of 30 kg, and its center of mass is three-eighths of the way up the ladder from the floor. If the coefficient of static friction between the ladder and the floor is 0.2, calculate how far a man of 80 kg can stand along the ladder without it slipping away at the floor. A) 3.7 m B) 6.3 m C) all the way to the top D) 5.4 m E) none of the above

Daniel and Jonathan are playing on the seesaw with their mother in the park. The 6-m long uniform board is hinged at its midpoint. If Daniel and Jonathan weigh 30kg and 20kg and sit at distances of 2m and 3m respectively from the fulcrum, calculate where their mother (mass = 60 kg) has to sit on the other side of the fulcrum for static equilibrium. A) 2.5 m B) 1.5 m C) 1.0 m D) 2.0 m E) none of the above