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## Homework Statement

A uniform metal pole of height ##30.0m## and a mass ##100kg## is initially standing upright but then falls over one side without its lower end sliding or losing contact with the ground.What is the linear speed of the pole's upper end just before impact ?

## Homework Equations

##τ=Frsinθ##

##τ=I∝##

## The Attempt at a Solution

I think there must be some ##F## force that the pole will start to fall.And there's also ##F'## force between pole and ground.

so total torque of the object will be (##I## take the touching point between pole and ground rotation axis).

So If total length is ##L## then I can write for this instance ##(t=0)##

##FL=τ(t=0)##

In between hitting the ground (lets call that time ##T##).The torque will be

##FL+mgsinθ\frac L 2=τ(0,T)##, but here sinθ will change every moment.

And in the impact it will be ##FL+mg\frac L 2=τ(T)##

then from here I tried to take a some time interval like when ##sinθ=\frac {\sqrt 2} {2}## and substract these values so that ##Fr## will cancel out but I don't know I stucked.

Then I thought I can just use the center of mass of pole's motion.It will make a parabola.And If I can calculate its speed when hits the ground I can easily calculate the end poing of pole.

Here I used normal projectile motion equations to find speed.but came out wrong.Maybe I am forgetting the centripetal force.Or Writing some equation wrong.

Thanks