Question

In the figure opposite, a wheel with a radius of 20 cm is on the surface and the position of point A on the edge of the wheel is shown in an instant. If after thisPosition, turn the wheel half a turn downwards, point A shifted a few centimeters. Use π =3.Find the displacement of point A

Answer 1

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:

`\begin{gathered} distance=(C)/(2)=(2\pi r)/(2)=\pi r \\ distance=3\cdot20 \\ distance=60\text{ cm} \end{gathered}`

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:

`\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}`

Therefore the displacement of point A is equal to 20√13 cm or 72.11 cm.