Q.
A girl walks 4km towards West, then she walks 3km in a direction 30∘ East of North and stops. Then, the girl’s displacement from her initial point of departures is
Let O and B be the initial and final positions of the girl, respectively.
Then, the girl's position can be shown as in the figure.
Now, we have OA=4i^ AB=i^∣AB∣cos60∘+j^∣AB∣sin60∘ (ABcos60∘ is component of AB along X -axis and ABsin60∘ is component of AB along Y -axis). =i^3×21+j^3×23=23i^+233j^
By the triangle law of vector addition, we have OB=AO+AB =(−4i^)+(23i^+233j^) =(−4+23)i^+233j^ =(2−8+3)i^+233j^=2−5i^+233j^
Hence, the girl's displacement from her initial point of departure is 2−5i^+233j^