# What is the displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward half a revolution ?

Q: What is the displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward half a revolution ? Take the radius of the wheel as R and the X -axis as the forward direction ?

Displacement of point of wheel $= \sqrt{X^2 + Y^2}$
$= \sqrt{(\pi R)^2 + (2R)^2}$
$= R\sqrt{\pi^2 + 4}$