A sail boat sails 2km east, then 5km 37 degrees south of east and finally an unknown displacement. If the final displacement of the boat from the starting point is 6km due east, determine the third displacement.

21 +5(cos371 - sin37j) +(unknown displacement)=6i

R=xî+y jIn x direction2î+5cos37î+xî = 6î 2+4+x =6X=0î means no displacement in x direction In y direction5 sin37 j = y j Y=3j3 km in north

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. So, unknown displacement is 3km due north