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HW 12 - Collisions Begin Date: 1/8/2024 12:01:00 AM -- Due Date: 4/15/2024 11:59:00 PM End Date: 4/22/2024 11:59:00 PM
(10\%) Problem 5: The diagram represents the collision in the \( x-y \) plane between identical hockey pucks, "Puck 1 " and "Puck 2". Prior to the collision, they are represented by dashed-outline circles, and afterwards they are represented by shaded discs. Initially, Puck 2 is at rest while Puck 1 has the initial velocity
\[
\begin{aligned}
\vec{v}_{1 i} & =v_{1 i, x} \hat{i}+v_{1 i, y} \hat{j} \\
& =(4.82 \mathrm{~m} / \mathrm{s}) \hat{i}+(4.14 \mathrm{~m} / \mathrm{s}) \hat{j}
\end{aligned}
\]
Post collision, Puck 1 moves with velocity \( \vec{v}_{1 f} \) at an angle \( \theta \) from the positive \( x \) axis, as drawn, while Puck 2 moves parallel to the positive \( y \) axis with the velocity
\[
\begin{aligned}
\vec{v}_{2 f} & =v_{2 f} \hat{j} \\
& =(1.39 \mathrm{~m} / \mathrm{s}) \hat{j}
\end{aligned}
\]
\( 33 \% \) Part (a) Using the symbols in the palette below, not their numeric equivalents, enter an expression, in Cartesian unit-vector notation, for the velocity of Puck 1 after the collision.
\[
\vec{v}_{1 f}=\mathrm{v}_{1 \text { ix }} \hat{i}
\]
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline\( \hat{i} \) & \( \hat{\mathbf{j}} \) & ( & ) & 7 & 8 & 9 & HOME \\
\hline\( \hat{\mathrm{k}} \) & \( \mathrm{v}_{1 \mathrm{ix}} \) & \( \uparrow^{\wedge} \) & \( \wedge \) & 4 & 5 & 6 & \( \leftarrow \) \\
\hline \( \mathrm{v}_{\text {liy }} \) & \( \mathrm{v}_{2 \mathrm{f}} \) & 1 & * & 1 & 2 & 3 & \( \rightarrow \) \\
\hline & & + & - & 0 & & . & END \\
\hline & & \( \sqrt{0} \) & \multicolumn{3}{|c|}{ BACKSPACE } & ? & CLEAR \\
\hline
\end{tabular}
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-Use conservation of momentum, and recall that momentum is conserved separately
in each direction
\( 78^{\circ} \mathrm{F} \)
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12:50 PM
\( 4 / 15 / 2024 \)
