A thin, uniform, rectangular sign hangs vertically above the door of a shop. The sign is hinged to a stationary horizontal rod along its top edge. The mass of the sign is 2.40 kilogram and its vertical dimension is 45.0 centimeter. The sign is swinging without friction, becoming a tempting target for children armed with snowballs. The maximum angular displacement of the sign is 25.0 degree on both sides of the vertical. At a moment when the sign is vertical and moving to the left, a snowball of mass 590 gram, traveling horizontally with a velocity of 160 cm/s to the right, strikes perpendicularly the lower edge of the sign and sticks there.
(a) Find the angular speed of the sign immediately before the impact.
rad/s
(b) Find its angular speed immediately after the impact.
rad/s
(c) Find the spattered sign will swing up through what maximum angle?
°