Answer:
3.324 km
Explanation:
d1 = 2 km south
d2 = 1.5 km at 37° east of south
Write the displacements in vector form
[tex]\overrightarrow{d_{1}}=-2\widehat{j}[/tex]
[tex]\overrightarrow{d_{2}}=1.5\left (Sin37\widehat{i}-Cos37\widehat{j} \right )=0.9\widehat{i}-1.2\widehat{j}[/tex]
The resultant displacement is given by
[tex]\overrightarrow{d} = \overrightarrow{d_{1}}+ \overrightarrow{d_{2}}[/tex]
[tex]\overrightarrow{d} = \left ( 0.9 \right )\widehat{i}+\left ( -2-1.2 \right )\widehat{j}[/tex]
[tex]\overrightarrow{d} = \left ( 0.9 \right )\widehat{i}+\left ( -3.2\right )\widehat{j}[/tex]
The magnitude of displacement is given by
[tex]d=\sqrt{0.9^{2}+\left ( -3.2 \right )^{2}}=3.324 km[/tex]
Thus, the bird has to travel 3.324 km in a straight line to return to its original place.
