Question

A car travels 32 km due north and

then 46 km in a direction 40° west of
north. Find the magnitude of the
car's resultant vector.
[ ? ] km
Round to the nearest tenth.

Answer 1

9514 1404 393

Answer:

73.5 km

Explanation:

The magnitude can be found from the law of cosines. The angle between the two vectors is 140°, so the magnitude is ...

c^2 = a^2 + b^2 -2ab·cos(C)

c^2 = 32^2 +46^2 -2·32·46·cos(140°) ≈ 5395.2348

c = √5395.2348 ≈ 73.452

The magnitude of the resultant vector is about 73.5 km.