Question

A sail boat sails 2km due East, 5km 37° South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6km due East, the third displacement is______.

Answer 1

S1 = 2i
S2 = 5Cos37i - 5Sin37j
S3 = Unknown displacement


S = S1 + S2 + S3

S3 = S - (S1 + S2)

S3 = 6i - (2i + 5Cos37i - 5Sin37j

S3 = 6i - 2i - 5*(4/5)i + 5*(3/5)j

S3 = 4i - 4i + 3j

S3 = 3j

Unknown displacement is 3km due north.

Answer 2

After the person has travelled 2 km , he moves 5 km making an angle 37 degree with horizontal or x axis

now we will do the component of 5 cos 37 degree and 5 sin 37 degree to get :

• 5 sin 37 degree = 3
• 5 cos 37 degree = 4

1. therefore he has travelled 4 km in positive X direction or 4 I cap
2. he has travelled 3 kilometre in positive y direction that is 4i cap.

In the question we are provided that the displacement from the starting point to final point is 6 km due east

and after doing the component we get that the person has travelled 4 km in X direction and 3 km in y direction .

Therefore his final displacement was 3 kilometre in in positive y direction.