Randall D. Knight — The Micro/Macro Connection: Problem Exercise_9

The molecules in a six-particle gas have velocities \[ \vec{v}_1 = (20\hat{i} - 30\hat{j})\text{ m/s} \] \[ \vec{v}_2 = (40\hat{i} + 70\hat{j})\text{ m/s} \] \[ \vec{v}_3 = (-80\hat{i} + 20\hat{j})\text{ m/s} \] \[ \vec{v}_4 = 30\hat{i}\text{ m/s} \] \[ \vec{v}_5 = (40\hat{i} - 40\hat{j})\text{ m/s} \] \[ \vec{v}_6 = (-50\hat{i} - 20\hat{j})\text{ m/s} \] Calculate (a) \(\vec{v}_{\text{avg}}\), (b) \(v_{\text{avg}}\), and (c) \(v_{\text{rms}}\).