The initial and final velocities of an object of mass 5 kg are \(u = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\) and \(v = \begin{pmatrix} 4 \\ 7 \end{pmatrix}\) respectively. Find the magnitude of its change in momentum.
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Correct Answer: Option A
Explanation:
Change in momentum = m (v - u)
= \(5 \times (\begin{pmatrix} 4 \\ 7 \end{pmatrix} - \begin{pmatrix} 1 \\ 3 \end{pmatrix})\)
= \(5 \times \begin{pmatrix} 3 \\ 4 \end{pmatrix}\)
= \(\begin{pmatrix} 15 \\ 20 \end{pmatrix}\)
\(|m(v - u)| = \sqrt{15^{2} + 20^{2}} = \sqrt{625} = 25\)
Change in momentum = m (v - u)
= \(5 \times (\begin{pmatrix} 4 \\ 7 \end{pmatrix} - \begin{pmatrix} 1 \\ 3 \end{pmatrix})\)
= \(5 \times \begin{pmatrix} 3 \\ 4 \end{pmatrix}\)
= \(\begin{pmatrix} 15 \\ 20 \end{pmatrix}\)
\(|m(v - u)| = \sqrt{15^{2} + 20^{2}} = \sqrt{625} = 25\)