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(A) The velocity of particle $A$ is constant along the $x$-axis: $\vec{V}_A = 1 \hat{i} \,m/s$. For particle $B$ moving along the $y$-axis, the positi

Vedclass · Accepted Answer

$\sqrt{5} \,m/s$

Vedclass · Answer

(A) The velocity of particle $A$ is constant along the $x$-axis: $\vec{V}_A = 1 \hat{i} \,m/s$. For particle $B$ moving along the $y$-axis, the position is $y = ct^2$. The velocity of particle $B$ is $\vec{V}_B = \frac{dy}{dt} \hat{j} = 2ct \hat{j}$. At $t = 1 \,s$ and $c = 1 \,m/s^2$, the velocity of particle $B$ is $\vec{V}_B = 2(1)(1) \hat{j} = 2 \hat{j} \,m/s$. The relative velocity of particle $A$ with respect to particle $B$ is $\vec{V}_{AB} = \vec{V}_A - \vec{V}_B = 1 \hat{i} - 2 \hat{j} \,m/s$. The speed is the magnitude of the relative velocity: $|\vec{V}_{AB}| = \sqrt{(1)^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5} \,m/s$.

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