Question

A hikers total displacement is 13 km at 35 degrees North East. If the hiker wishes to return to his starting point on a trail that goes due South and then due West, what will be the total distance he travels on his return trip? Draw a diagram to show the directions and distances he travels .

Answer 1

18.1 km

Step-by-step explanation:

The problem can be solved by resolving the vector representing the displacement into its components along the north-south and east-west directions.

Look at the figure below: the displacement is the vector that connects A (starting point) to B (ending point), while the distance covered during the return trip is the sum of the length of the two components along the north-south and east-west direction.

Using vector rules, we find the magnitude of the two components:

East-west:

`d_x = 13 cos 35^(\circ)=10.6 km`

North-south:

`d_y = 13 sin 35^(\circ)=7.5 km`

So the total distance covered during the return trip is

`d=d_x + d_y = 10.6 + 7.5 = 18.1 km`