A car travels 20.2 km due north and then

Question

31.3 km in a direction φ = 61.2◦ west of north.

Find the magnitude of the car’s resultant
displacement.

Then Calculate the direction of the car’s resultant displacement, measured counterclockwise from the northerly direction.

Answer 1

α=180-61.2=118.8°
Cosine Law
d=sqrt{20.2²+31.3²-2•20.2•31.3•cos118.8°} =
=44,7 km
Sine Law
31.3/sinθ=44.7/sin118.8°
sinθ=31.3 •sin118.8°/44.7=0.61
θ= 37.9°