On an ice skating rink, a girl of mass 50. kg stands stationary, face to face with a boy of mass 80. kg. The children push off of one another, and the boy moves away with a velocity of -4.0 m/s. To two significant digits (the tenths place), what is the final velocity of the girl? m/s

Agas is contained in a vertical, frictionless piston–cylinder device. the piston has a mass of 3.2 kg and a cross-sectional area of 35 cm2. a compressed spring above the piston exerts a force of 190 n on the piston. if the atmospheric pressure is 95 kpa, determine the pressure inside the cylinder.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)