Question

A hiker begins a trip by first walking 17 km southeast from her base camp. On the second day, she walks 49.7 km in a direction 66.7 ◦ north of east, at which point she discovers a forest ranger’s tower. Determine the y component of the total displacement.

Answer 1

Answer:Total displacement =36.63 m

Explanation: For the y component of the displacement only the north and south displacement is to evaluated

The displacement in the south can be taken as negative

The first displacement of hiker is 45 degree in 4rth quadrant as described in the question as "south East"

if we take the distance 17 km as hypotenuse then to find y component we will find the perpendicular

`-sin 45=perpendicular / 17\\perpendicular=d1\\d1=-17*sin 45\\d1=-12.02m`

similarly the angle for the second displacement in the north is given as 66.7 degree and we will use the same approach

This is in the first quadrant hence the displacement is positive

`sin 66.7=perpendicular / 49.7\\perpendicular=d2\\d2=49.7*sin 45\\d2=45.646m`

Total displacement =d1+d2

Total displacement =36.63 m in the north