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.

Options

A. `3 km` North
B. `4 km`, South
C. `5 km`, East
D. `3 km`,West

Answer

A

Explanation

Given resultant displacement is `6 km` due east Which may be expressed as `6hat(i)`

Given displacements are:
(i) 2 km due east or `2 hat(i)`
(ii) `5 km 37^(@)`south of east its componets
along x-axis `= 5 cos 37^(@)= 5xx4/5= 4hat` (i)
along y-axis `= 5 sin 37^(@)= 5xx3/5= -3hat(j)`
(iii) unknown displacement let it 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
`a= 0` and `b=3`
`:.` unknown displacement `= 3hat(j)`