Question

At some point as you are hiking near a lake, you determine that your campsite is 1.50 km away from you in the direction 30.0 ◦ E of N. However, to get back to your campsite, you will need to walk around the lake. You set off due north and walk for 600 m. You then turn in the direction 20.0 ◦ W of N and walk an additional 1.20 km, before turning and walking directly to your campsite. How far and in what direction was the last leg of your hike?

Answer 1

Solution:

Let + x axis in direction of East and + y axis in direction of North.

Required net displacement = 1500 m towards 30^o E of N

First displacement = 600 m towards north

second displacement = 1200 m towards 20^o W of N

     

third unknown displacement =

Vector sum of all three displacents gives net displacement

  

third displacement = 705 m towards 52^o E of S