question_answer

In the above problem, if the cyclist reaches a point 'Z' as shown in the figure, find the distance travelled and magnitude of displacement of the cyclist.

Answer:

                  Distance covered by cyclist = Quadrant of circle \[=\frac{1}{4}\times Circumference\,\,of\,\,circle\] \[=\frac{1}{4}\times 2\pi r=\frac{\pi r}{2}\] Initial position\[=x,\] Final position = z Magnitude of displacement\[=xz=?\] Considering right triangle oxz, we have \[xz=\sqrt{{{(ox)}^{2}}+{{(oz)}^{2}}}\] \[=\sqrt{{{(r)}^{2}}+{{(r)}^{2}}}\]              (from Pythagoras theorem) \[=\sqrt{2{{r}^{2}}}=\sqrt{2}r\]