Question:
Car A is moving to the east with a speed of 30 km/hr, and car B is moving to the north with the same speed. What is the velocity of car B as measured in car A?
Car A is moving to the east with a speed of 30 km/hr, and car B is moving to the north with the same speed. What is the velocity of car B as measured in car A?
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Subtract the vector of the observer (A) from the vector of the object (B).
Updated On: May 12, 2026
- 42 km/hr, $45^{\circ}$ north of west
- 42 km/hr, $45^{\circ}$ east of north
- 60 km/hr, $45^{\circ}$ south of east
- 42 km/hr, $45^{\circ}$ south of east
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Relative velocity of B with respect to A is $\vec{v}_{BA} = \vec{v}_{B} - \vec{v}_{A}$.
Step 2: Meaning
Let East be $\hat{i}$ and North be $\hat{j}$. $\vec{v}_{A} = 30\hat{i}$, $\vec{v}_{B} = 30\hat{j}$. $\vec{v}_{BA} = 30\hat{j} - 30\hat{i}$.
Step 3: Analysis
Magnitude $= \sqrt{(-30)^{2} + 30^{2}} = 30\sqrt{2} \approx 30 \times 1.414 = 42.42 \approx 42$ km/hr. Direction: The vector has a negative x-component (West) and a positive y-component (North). Since components are equal, the angle is $45^{\circ}$ North of West.
Step 4: Conclusion
Velocity is 42 km/hr at $45^{\circ}$ North of West. Final Answer: (A)
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