Question

Caroline is geocaching in the woods, she walks 13 km due east, then 18 km north, finally 3 km west to find the cache.

Answer 1

Answer:

$\vec{a}=(10,18).$

$2\sqrt{106}\approx20.6\ km.$

Step-by-step explanation:

Let the initial Caroline's location be at the origin (0,0) and the directions be:

• north - positive y-direction;
• south - negative y-direction;
• east - positive x-direction;
• west - negative x-direction.

1. Caroline walks 13 km due east, then her location is (13,0).

2. Caroline walks 18 km to the north, then her location is (13,18).

3. Caroline walks 3 km west, then her location is (10,18).

Thus, the component form of the vector containing her final destination is

$\vec{a}=(10,18).$

If Caroline’s friend travels the shortest root to the cache, she will walk

$\sqrt{10^2+18^2}=\sqrt{10+324}=\sqrt{424}=2\sqrt{106}\approx20.6\ km.$