Answer
$$1.68\ \mathrm{m}$$
Work Step by Step
The point $P$ is displaced vertically by $2 R,$ where $R$ is the radius of the wheel. It is displaced horizontally by half the circumference of the wheel, or $\pi R .$
since $R=0.450 \mathrm{m} $,the horizontal component of the displacement is 1.414 $\mathrm{m}$ and the vertical component of the displacement is 0.900 $\mathrm{m} .$ If the $x$ axis is horizontal and the $y$ axis is vertical, the vector displacement (in meters) is $\vec{r}=(1.414 \hat{\mathrm{i}}+0.900 \hat{\mathrm{j}}) .$
The displacement has a magnitude of
$$|\vec{r}|=\sqrt{(\pi R)^{2}+(2 R)^{2}}=R \sqrt{\pi^{2}+4}=1.68 \mathrm{\ m}$$
