A 6.0 x 105 kg space probe is traveling at speed vo through deep space. Retrorockets are fired to slow down the probe and they generate a force of - 1.125 x 106 N over a distance of 3000 km. The final speed of the probe is found to be 3.0 x 103 m/s. Calculate the (initial) speed vo .

Two masses are connected by a rope that hangs over a pulley as shown below. the pulley is a uniform cylinder of radius 푅=0.381meters and mass 푀=3.1푘푔. initially 푚"is on the ground and 푚#rests 2.5 meters above the ground. if the system is released, use conservation of energy to determine the speed of 푚#just before it strikes the ground. assume the pulley bearing is frictionless.