Question

The relative velocity of a car ‘A’ with respect to car B is 30√2 m/s due North-East. The velocity of car ‘B’ is 20 m/s due south. The relative velocity of car ‘C’ with respect to car ‘A’ is 10√2 m/s due North-West. The speed of car C and the direction (in terms of angle it makes with the east).

• A. 20√2 m/s, 45⁰
• B. 20√2 m/s, 135⁰
• C. 10√2 m/s, 45⁰
• D. 10√2 m/s, 135⁰

Answer 1

Answer: (D)

10√2 m/s, 135⁰

Answer 2

${\overrightarrow{v}}_{A} - {\overrightarrow{v}}_{B} = 30\sqrt{2}\left( \cos 45^{o}\widehat{i} + \sin 45^{o}\widehat{j} \right)$= ($30\widehat{i} + 30\widehat{j}$) m/s

${\overrightarrow{v}}_{B} = \left( - 20\widehat{j} \right)$m/s

${\overrightarrow{v}}_{C} - {\overrightarrow{v}}_{A} = 10\sqrt{2}\left( - \cos 45^{o}\widehat{i} + \sin 45^{o}\widehat{j} \right)$=$\left( - 10\widehat{i} + 10\widehat{j} \right)$ m/s

Hence, (1) is correct.