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# Vprob1

last edited by 14 years, 3 months ago

# Problem 1 of 3

A ship travels 15 km on a bearing of 070°. It then changes direction and travels 22 km on a bearing of 200°.

(a) Draw a vector diagram modelling this situation.

(b) How far is the ship from its starting point?

Solution

(a) (b) To solve this problem we can use the sin law or the cosine law to find the distance of AC(A is the starting point, B is the point where they changes direction and C is the final position of the ship).

Sine Law Solution

a/Sin A = b/Sin B

22 Km/Sin 87.08° = b/Sin 50°

b*Sin 87.08° = 22 km*Sin50°

b = (22 km*Sin50°)/Sin87.08°

b = 16.87 km

Cos Law Solution

b2 = a2+c2-2*a*c*Cos B

b2 = (222+152)-(2*22*15*Cos 50°)

b2 = 709-424.23

b2 = 284.77

b = 16.87 km

The ship is 16.87 km away from the starting point

(c) There are 3 ways to anwers this question, we can use the bearing method, the degrees and compass method or the compass and degrees method.

Using the Bearing Method

The ship must head 16.87 km at a bearing of 292.92° or at 293°

Using the Degrees and Compass Direction Method

22.92° north of west or 67.08° west of north

Using the Compass Direction and Degrees

North 22.92° West or West 67.08° North