Question

Please help! Vectors and angles

A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree

Answer 1

You're right, It was A!

Answer 2

The velocity of the ship = 22 ∠157° = (22 cos 157°) i+ (22 sin 157°) j

The velocity of current = 5 ∠213° = (5 cos 213°) i+ (5 sin 213°) j

So, the resultant velocity = 22 ∠157° + 5 ∠213°
= (22 cos 157°) i+ (22 sin 157°) j + (5 cos 213°) i+ (5 sin 213°) j
= (22 cos 157° + 5 cos 213°) i + (22 sin 157° + 5 sin 213°) j
= -24.444 i + 5.873 j
= 25.14 ∠166.5°

The correct answer is option (1)
1) 25 knots at 166.5 degree