Question

# One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 1.50 km. They start at the west side of the lake and head due south to begin with. (a) What is the distance they travel? (b) What are the magnitude and direction (relative to due east) of the couple 's displacement?

Solution

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a) The total distance equals three quarters of the lake circumference, so if the lake has a radius of $R=1.5$ km, the total distance would be:

\begin{align*} d&=\dfrac{3}{4} \left[ 2\pi R\right]\\ &=\dfrac{3}{4} \left[ 2\pi (1.5)\right]\\ &=7.0686 \mathrm{~km} \end{align*}

$\boxed{d=7.0686 \mathrm{~km}}$

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