Question

Following a treasure map, Captain Jack Sparrow walks north for 100 m, then turns toward 30 degrees south of east and walks for 80.0 m, then turns toward 45 degrees north of east and walks for 150 m. Find the magnitude of Captain Sparrow's displacement.

Answer 1

Using vector addition

V1 = 100 m north = 100 j

V2 = 80 m towards 30 deg south of east = 80*cos 30 deg i - 80*sin 30 deg j

V3 = 150 m towards 45 deg north of east = 150*cos 45 deg i + 150*sin 45 deg j

Adding above vectors

Vnet = V1 + V2 + V3

Vnet = 100 j + (80*cos 30 deg i - 80*sin 30 deg j) + (150*cos 45 deg i + 150*sin 45 deg j)

Vnet = (80*cos 30 deg i + 150*cos 45 deg i) + (100 j - 80*sin 30 deg j + 150*sin 45 deg j)

Vnet = (69.28 + 106.07) i + (100 - 40 + 106.07) j

Vnet = 175.35 i + 166.07 j

Magnitude of displacement will be

|Vnet| = sqrt (175.35^2 + 166.07^2) = 241.05 m

Please Upvote.