Interpret the motion on the circle

The person moves from $A$ to $B$ along a circular arc of length $60\,\text{m}$.

From the figure/context, the arc corresponds to a central angle of $270^\circ$, so the smaller angle between radii $OA$ and $OB$ is: $360^\circ - 270^\circ = 90^\circ$

Find the radius of the circle

Arc length is given by $s = r\theta$ where $\theta$ is in radians.

Here, $s=60, \qquad \theta=270^\circ=\frac{3\pi}{2}$

So, $60 = r\cdot \frac{3\pi}{2}$ $r = \frac{60\cdot 2}{3\pi} = \frac{40}{\pi}$

Using $\pi \approx \frac{22}{7}$, $r \approx \frac{40}{22/7} = \frac{280}{22} \approx 12.7\,\text{m}$

Find the displacement

Displacement is the straight-line distance from $A$ to $B$, i.e. the chord $AB$.

For central angle $90^\circ$, chord length is $AB = \sqrt{r^2+r^2} = r\sqrt{2}$

Hence, $AB \approx 12.7\times 1.414 \approx 18\,\text{m}$

Closest option: $\boxed{19\,\text{m}}$

Check options

• A: $42\,\text{m}$ ❌
• B: $47\,\text{m}$ ❌
• C: $19\,\text{m}$ ✅
• D: $40\,\text{m}$ ❌

Comparison with stored answer

My derived answer is Option C: $19\,\text{m}$.

The stored correct answer is B: $47\,\text{m}$, which does not match.

So the stored answer appears incorrect, likely due to misreading the angle in the figure.