Car A is moving to the East with a speed of 3 | vedclass

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(A) Given that, velocity of car $A$ is $\vec{v}_A = 30 \hat{i} 	ext{ km/h}$ (toward East).For car $B$, velocity is $\vec{v}_B = 30 \hat{j} 	ext{ km/

Vedclass · Accepted Answer

$42 	ext{ km/h}, 45^{\circ}$ North of West

Vedclass · Answer

(A) Given that, velocity of car $A$ is $\vec{v}_A = 30 \hat{i} 	ext{ km/h}$ (toward East).For car $B$, velocity is $\vec{v}_B = 30 \hat{j} 	ext{ km/h}$ (toward North).The velocity of car $B$ as measured from car $A$ is the relative velocity $\vec{v}_{BA} = \vec{v}_B - \vec{v}_A$.$\vec{v}_{BA} = 30 \hat{j} - 30 \hat{i} 	ext{ km/h}$.The magnitude of $\vec{v}_{BA}$ is $|\vec{v}_{BA}| = \sqrt{(-30)^2 + (30)^2} = \sqrt{900 + 900} = \sqrt{1800} = 30\sqrt{2} \approx 42 	ext{ km/h}$.The direction is given by $	an 	heta = \frac{v_{y}}{v_{x}} = \frac{30}{-30} = -1$. This corresponds to an angle of $135^{\circ}$ from the positive $x$-axis (East).Since the vector points in the second quadrant (negative $x$, positive $y$), it is $45^{\circ}$ North of West.

Car $A$ is moving to the East with a speed of $30 \text{ km/h}$, and car $B$ is moving to the North with the same speed. What is the velocity of car $B$ as measured from car $A$?

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