In order to calculate the displacement of point A, first let's calculate the distance the wheel will move, using the formula for half the perimeter of a circumference:
[tex]\begin{gathered} distance=\frac{C}{2}=\frac{2\pi r}{2}=\pi r \\ distance=3\cdot20 \\ distance=60\text{ cm} \end{gathered}[/tex]
Now, let's draw an image with the initial and final position of point A:
The displacement D is given by the hypotenuse of the blue triangle, so we have:
[tex]\begin{gathered} D^2=distance^2+(2r)^2 \\ D^2=60^2+40^2 \\ D^2=3600+1600 \\ D^2=5200 \\ D=20\sqrt[]{13}=72.11 \end{gathered}[/tex]
Therefore the displacement of point A is equal to 20√13 cm or 72.11 cm.
