Asolid wood door 1.00m wide and 2.00m high is hinged along one side and has a total mass of 43.0kg. initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.700kg, traveling perpendicular to the door at 13.0m/s just before impact.
a) find the angular speed of the door.
b) does the mud make a significant contribution to the moment of inertia?

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.