Question

TOW CARS A AND B MOVING ALONG INA A STRIGHT LINE. Car A is moving at a speed of 80 km/h while car Bi s moving at speed 50km/h in same direction.

find the magnitude and direction of

1) the relative velocity of car A with respet to B

2)the relative velocity of car B with respect To A

Answer 1

$$\begin{gathered} 1-\mathrm{Relative}\mathrm{velocity}\mathrm{of}\mathrm{car}\mathrm{A}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{B}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{Velocity}\mathrm{of}\mathrm{car}\mathrm{A}+(-\mathrm{velocity}\mathrm{of}\mathrm{car}\mathrm{B}) \\ =80+[-(-50\left)\right] \\ =130\mathrm{km}/\mathrm{h} \\ \mathrm{Positive}\mathrm{velocity}\mathrm{shows}\mathrm{that}\mathrm{for}\mathrm{a}\mathrm{person}\mathrm{in}\mathrm{car}\mathrm{B},\mathrm{car}\mathrm{A}\mathrm{will}\mathrm{appear}\mathrm{to}\mathrm{move}\mathrm{in}\mathrm{the}\mathrm{same}\mathrm{direction}\mathrm{with}\mathrm{speed}\mathrm{of}\mathrm{sum}\mathrm{of}\mathrm{their}\mathrm{individual}\mathrm{speed}. \\ 2-\mathrm{Relative}\mathrm{velocity}\mathrm{of}\mathrm{car}\mathrm{B}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{A}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{Velocity}\mathrm{of}\mathrm{car}\mathrm{B}+(-\mathrm{velocity}\mathrm{of}\mathrm{car}\mathrm{A}) \\ =-50+(-80)=-130\mathrm{km}/\mathrm{h} \\ \mathrm{Here},\mathrm{negative}\mathrm{sign}\mathrm{shows}\mathrm{that}\mathrm{car}\mathrm{B}\mathrm{will}\mathrm{appear}\mathrm{to}\mathrm{move}\mathrm{with}130\mathrm{km}/\mathrm{h}\mathrm{in}\mathrm{opposite}\mathrm{direction}\mathrm{to}\mathrm{car}\mathrm{A}. \end{gathered}$$