A dead tree is initially stationary and there is a 30.0-degreeree angle between

Question

A dead tree is initially stationary and there is a 30.0-degreeree angle between the tree and the vertical. The roots finally give way and the tree topples to the ground (rotating on an axis that is parallel to the level ground and intersecting the base of the tree perpendicularly through the base of the tree. The length of the tree is 30.0 m. How fast is the top of the tree moving (in m/s) just before it hits the ground? Model the tree as straight, rigid rod, and ignore friction and air resistance.

Explanation / Answer

let the speed of tip=v w=v/l mgl*cos(30)/2=0.5*I*w^2 I=ml^2/3 mgl*cos(30)=(m*l^2/3)*v^2/l^2 v=sqrt(3gl*cos(30))=27.65 m/s

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