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A ladder AB rests against a vertical wall 0A. The foot 'B' of the ladder is pulled away with constant speed V
a) show that the midpoint of the ladder describes the arc of a circle of radius a/2
b) Find the velocity and speed of the midpoint of the ladder at the instant B is distant b
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Let A= (0,y) be the upper endpoint of the ladder and
let B= (x,0) be its lover end point in coordinate plane with the origin at (0,0).
Then x^2 + y^2 = the square of the ladder length d = constant value .
The coordinates of the middle point of the ladder is (x/2,y/2).
Since x^2 + y^2 = const, we have + = , which is also a constant value.
It means that the midpoint of the ladder lies and moves on the circle of the radius , centered at the origin.
This statement DOES NOT DEPEND on the speed V of the ladder along the earth surface.
This speed can be non-uniform (not constant) - it does not changes the statement.
So, question (a) is answered.