• # question_answer The relatives velocity of a car A with respect to car B is $30\sqrt{2}\,m/s$ due north-east. The velocity of car B is $20m/s$ due south. The relative velocity of car C with respect to car A is $10\sqrt{2}m/s$ due north weast. The speed of car c and the direction (in terms of angle it makes with the east) are respectively: A)  $20\sqrt{2}m/s,\,{{45}^{o}}$     B)  $20\sqrt{2}m/s,\,{{135}^{o}}$C)  $10\sqrt{2}\,m/s,\,{{45}^{o}}$D)  $10\sqrt{2}\,m/s,\,{{135}^{o}}$

From the diagram (above), we get             ${{V}_{CA}}={{V}_{A}}-{{V}_{B}}$                 $=30\sqrt{2}\,(\cos {{45}^{o}}i+\sin {{45}^{o}})$                 $=(30i+30j)m/s$                 ${{V}_{B}}=(-20j)m/s$ (given)                 ${{V}_{CA}}={{V}_{C}}-{{V}_{A}}$                 $=10\sqrt{2}\,(-\cos \,{{45}^{o}}i+\sin {{45}^{o}}j)$                 $=(-10i+10j)m/s$                 ${{V}_{C}}=20i+20j$                 $|{{V}_{C}}|\,\,=\sqrt{{{20}^{2}}+{{20}^{2}}}=20\sqrt{2}$ and       $\tan \theta =20/20$  $\Rightarrow$  $\theta ={{45}^{o}}$