Question

A) If you walk 14 steps at an angle of 139 (relative to the positive x-axis) and then turn and go 63 steps at an angle of 277, how far from the starting point will you end up?

B) If a boat moves at 25 m/s at an angle of 145 in an ocean current of 28 m/s at an angle of 198 while the wind is pushing it at 9 m/s at an angle of 284 , what is the magnitude of the real velocity of the boat? (Tip: add the three vectors with the four step method)

Answer 1

(a) We have to add the two vectors. (It is assumed that the 277 degrees is with respect to the +x axis only). The resultant is given by,

Here the angle is between the two vectors when the vectors are placed tail to tail, which is 277-139 = 138 degrees. Substituting values we get,

Therefore we will be 53.42 steps away from the starting point.

(b) Each of the vectors can be written in component form as,

Substituting values we get the vectors as,

Adding the vectors we will get the resultant vector as,

Hence the magnitude of the resultant velocity is,

Therefore the real velocity of the boat is 45.03 m/s.