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,determine the third displacement.

Answer

`3hat(j)`

Explanation

Given that the resultant displacement is `6km` due east which may be expresses as `6hat(i)`.
Given displacement are:
a. `2km` due east or `2hat(i)`
b. `5km 37^(@)` south of east its components are :
Along x-axis `=5 cos 37^(@)=5xx4/5=4hat(i)`
Along y-axis `= 5 sin 37^(@)=5xx3/5=13hat(j)`
c. Let the unknown displacement be `ahat(i)+bhat(j)`
`:. 2hat(i)+4hat(i)-3hat(j)+ahat(i)+bhat(j)=6hat(i)`
`:. 6hat(i)+ahat(i)-3hat(j)+bhat(j)=6hat(i)`
Comparing the two sides, we get `a=0` and `b=3`.
Therefore, unknown displacement `=3hat(j)`