Suppose a small airplane is flying at a speed of 175 miles per hour...

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# Suppose a small airplane is flying at a speed of 175 miles per hour...

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<p>sec</p><p><span class="eqneditor-formula" data-value="\vec{v}=-105.3i+139.8j"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut" style="height:.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em;">s</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body"><span class="overlay" style="height:.714em;width:.471em;"><svg width="0.471em" height="0.714em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5 3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11 10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63 -1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1 -7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59 H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359 c-16-25.333-24-45-24-59z"></path></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em;"></span><span class="mrel">s</span><span class="mspace" style="margin-right:.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:.74285em;vertical-align:-.08333em;"></span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:.2222222222222222em;"></span><span class="mbin">s</span><span class="mspace" style="margin-right:.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:.85396em;vertical-align:-.19444em;"></span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord mathnormal" style="margin-right:.05724em;">s</span></span></span></span></span></p><p><span class="eqneditor-formula" data-value="\vec{w}=-40i"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut" style="height:.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.02691em;">s</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body"><span class="overlay" style="height:.714em;width:.471em;"><svg width="0.471em" height="0.714em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5 3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11 10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63 -1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1 -7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59 H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359 c-16-25.333-24-45-24-59z"></path></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em;"></span><span class="mrel">s</span><span class="mspace" style="margin-right:.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:.74285em;vertical-align:-.08333em;"></span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord mathnormal">s</span></span></span></span></span></p><p> </p><p>sec</p><p><span class="eqneditor-formula" data-value="\vec{v}+\vec{w}=-145.3i+139.8j"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut" style="height:.79733em;vertical-align:-.08333em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em;">s</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body"><span class="overlay" style="height:.714em;width:.471em;"><svg width="0.471em" height="0.714em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5 3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11 10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63 -1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1 -7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59 H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359 c-16-25.333-24-45-24-59z"></path></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em;"></span><span class="mbin">s</span><span class="mspace" style="margin-right:.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.02691em;">s</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body"><span class="overlay" style="height:.714em;width:.471em;"><svg width="0.471em" height="0.714em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5 3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11 10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63 -1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1 -7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59 H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359 c-16-25.333-24-45-24-59z"></path></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em;"></span><span class="mrel">s</span><span class="mspace" style="margin-right:.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:.74285em;vertical-align:-.08333em;"></span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:.2222222222222222em;"></span><span class="mbin">s</span><span class="mspace" style="margin-right:.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:.85396em;vertical-align:-.19444em;"></span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord mathnormal" style="margin-right:.05724em;">s</span></span></span></span></span></p><p> </p><p>sec</p><p><span class="eqneditor-formula" data-value="\left |\vec{v}+\vec{w} \right |=202\frac{mi}{hr}"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">s</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.03588em;">s</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body"><span class="overlay" style="height:.714em;width:.471em;"><svg width="0.471em" height="0.714em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5 3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11 10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63 -1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1 -7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59 H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359 c-16-25.333-24-45-24-59z"></path></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2222222222222222em;"></span><span class="mbin">s</span><span class="mspace" style="margin-right:.2222222222222222em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:.02691em;">s</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body"><span class="overlay" style="height:.714em;width:.471em;"><svg width="0.471em" height="0.714em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5 3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11 10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63 -1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1 -7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59 H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359 c-16-25.333-24-45-24-59z"></path></svg></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">s</span></span><span class="mspace" style="margin-right:.2777777777777778em;"></span><span class="mrel">s</span><span class="mspace" style="margin-right:.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.200664em;vertical-align:-.345em;"></span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.855664em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight" style="margin-right:.02778em;">s</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight">s</span></span></span></span></span><span class="vlist-s">s</span></span><span class="vlist-r"><span class="vlist" style="height:.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p> </p><p>sec</p><p><span class="eqneditor-formula" data-value="\theta =313.9^{\circ}"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut" style="height:.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:.02778em;">s</span><span class="mspace" style="margin-right:.2777777777777778em;"></span><span class="mrel">s</span><span class="mspace" style="margin-right:.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:.674115em;vertical-align:0em;"></span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord">s</span><span class="mord"><span class="mord">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.674115em;"><span style="top:-3.063em;margin-right:.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">s</span></span></span></span></span></span></span></span></span></span></span></span></span></p>

## Step-by-step explanation

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