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?

Explanation:

given,

door dimension  = 1 m x 2 m

mass of = 43 Kg

Mass of dust = 0.7 Kg

speed of the door = 13 m/s

a) from conservation of angular momentum  

b) angular speed without considering mud

there is no significant contribution of mud in moment of inertia .

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

i believe the answer is a