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

Verified
Step 1
1 of 4

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*}

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

Free body diagram.

## Recommended textbook solutions

#### Cutnell and Johnson Physics

9th EditionISBN: 9780470879528 (1 more)John D. Cutnell, Johnson
2,467 solutions

#### Fundamentals of Physics

8th EditionISBN: 9780471758013Halliday, Resnick, Walker
9,467 solutions

#### Fundamentals of Physics

10th EditionISBN: 9781118230718David Halliday, Jearl Walker, Robert Resnick
8,950 solutions

#### Fundamentals of Physics, Extended

11th EditionISBN: 9781119306856 (1 more)David Halliday, Jearl Walker, Robert Resnick
9,568 solutions