Solution 8.9b

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We use \displaystyle \mathbf{v}=\mathbf{u}+\mathbf{a}t \ with

\displaystyle \mathbf{u}=15\mathbf{i}+18\mathbf{j}\text{ m}{{\text{s}}^{\text{-1}}}

\displaystyle \mathbf{a}=-10\mathbf{j}

\displaystyle t=3\text{ s}

giving \displaystyle \mathbf{v}=15\mathbf{i}+18\mathbf{j}+(-10\mathbf{j} )\times 3

Simplifying \displaystyle \mathbf{v}=15\mathbf{i}+18\mathbf{j}-30\mathbf{j}=15\mathbf{i}-12\mathbf{j}

The speed \displaystyle S is the magnitude of this velocity.

\displaystyle S=\sqrt{{{15}^{2}}+{{\left( -12 \right)}^{2}}}=\sqrt{225+144}=19\textrm{.}2\ \text{m}{{\text{s}}^{-1}}