Question

A boat heads due North for 3.00 km to reach a red buoy. It then changes direction and heads in a direction of 30.0 degrees South of East for a distance of 4.66 km to reach a blue buoy. The boat changes direction again and heads to a green buoy which is 1.00 km due East of the boat’s starting position. What must be the boat’s displacement to go from the blue buoy to the green buoy? Express that displacement as the distance travelled in a direction specified as an angle East or West of South.

Answer 1

Position of B :  

x = 4.66*cos 30 = 4.036  

y = 3-4.66*sin 30 = 3-2.33 = 0.67  

BC = √y^2+(x-1)^2 = √0.67^2+3.036^2 = 3.109  

heading = arctan y/(x-1) = arctan 0.67/(3.036) = 12.44° south of west

hope this helps :)