AI Summary of "Gerak Parabola | Fisika Kelas 10 - KHATULISTIWA MENGAJAR"
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Definition and Characteristics of Parabolic Motion</strong><br/>📌 <span class="yellow-highlight font-semibold">Parabolic motion</span> (Gerak Parabola) describes the movement of an object thrown upwards, resulting in a curved path resembling a parabola.<br/>📐 This motion involves two axes: the <span class="yellow-highlight font-semibold">horizontal axis (X)</span> and the <span class="yellow-highlight font-semibold">vertical axis (Y)</span>.<br/>🏀 An example given is shooting a three-point basketball shot, where the trajectory forms a curve.</p>
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Mathematical Calculation Example</strong><br/>🔢 For a basketball thrown at an elevation angle of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>30</mn><mo lspace="0em" rspace="0em">∘</mo></msup></mrow><annotation encoding="application/x-tex">30^{\circ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6741em;"></span><span class="mord">3</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∘</span></span></span></span></span></span></span></span></span></span></span></span> with an initial velocity (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">v_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mtext> m/s</mtext></mrow><annotation encoding="application/x-tex">30 \text{ m/s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">30</span><span class="mord text"><span class="mord"> m/s</span></span></span></span></span>:<br/>➡️ The initial velocity component on the X-axis (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mn>0</mn><mi>x</mi></mrow></msub></mrow><annotation encoding="application/x-tex">v_{0x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) is calculated as <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mn>0</mn></msub><mo>⋅</mo><mi>cos</mi><mo></mo><mo stretchy="false">(</mo><mtext>angle</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">v_{0} \cdot \cos(\text{angle})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5945em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cos</span><span class="mopen">(</span><span class="mord text"><span class="mord">angle</span></span><span class="mclose">)</span></span></span></span>.<br/>➡️ Substituting values: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mn>0</mn><mi>x</mi></mrow></msub><mo>=</mo><mn>30</mn><mo>⋅</mo><mi>cos</mi><mo></mo><mo stretchy="false">(</mo><msup><mn>30</mn><mo lspace="0em" rspace="0em">∘</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mn>30</mn><mo>⋅</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac><mo>=</mo><mn>15</mn><msqrt><mn>3</mn></msqrt><mtext> m/s</mtext></mrow><annotation encoding="application/x-tex">v_{0x} = 30 \cdot \cos(30^{\circ}) = 30 \cdot \frac{\sqrt{3}}{2} = 15\sqrt{3} \text{ m/s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">cos</span><span class="mopen">(</span><span class="mord">3</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∘</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.383em;vertical-align:-0.345em;"></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:1.038em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.399em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9128em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight">3</span></span></span><span style="top:-2.8728em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702<br/>c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14<br/>c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54<br/>c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10<br/>s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429<br/>c69,-144,104.5,-217.7,106.5,-221<br/>l0 -0<br/>c5.3,-9.3,12,-14,20,-14<br/>H400000v40H845.2724<br/>s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7<br/>c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z<br/>M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1272em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1572em;vertical-align:-0.25em;"></span><span class="mord">15</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">3</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702<br/>c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14<br/>c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54<br/>c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10<br/>s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429<br/>c69,-144,104.5,-217.7,106.5,-221<br/>l0 -0<br/>c5.3,-9.3,12,-14,20,-14<br/>H400000v40H845.2724<br/>s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7<br/>c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z<br/>M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mord text"><span class="mord"> m/s</span></span></span></span></span>.<br/>⬆️ The horizontal velocity remains constant, meaning the velocity at the highest point is still <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>15</mn><msqrt><mn>3</mn></msqrt><mtext> m/s</mtext></mrow><annotation encoding="application/x-tex">15\sqrt{3} \text{ m/s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1572em;vertical-align:-0.25em;"></span><span class="mord">15</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">3</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702<br/>c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14<br/>c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54<br/>c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10<br/>s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429<br/>c69,-144,104.5,-217.7,106.5,-221<br/>l0 -0<br/>c5.3,-9.3,12,-14,20,-14<br/>H400000v40H845.2724<br/>s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7<br/>c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z<br/>M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mord text"><span class="mord"> m/s</span></span></span></span></span>.</p>
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Real-World Applications of Parabolic Motion</strong><br/>🚀 Parabolic motion principles are observed in everyday activities beyond sports, including <span class="yellow-highlight font-semibold">rocket launches</span> in technology.<br/>🌱 When watering plants, the trajectory of the water forms a parabola to cover a <span class="yellow-highlight font-semibold">wider area</span>.<br/>🎯 In archery, the <span class="yellow-highlight font-semibold">arrow released by the archer</span> follows a parabolic path before hitting the target.<br/>⛲ Water flowing from a fountain also demonstrates parabolic motion as the stream moves from one point to another before returning to the pool.</p>
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Key Points & Insights</strong><br/>➡️ <span class="yellow-highlight font-semibold">Parabolic motion is a common physics phenomenon</span> with numerous practical applications across sports, technology, and daily life.<br/>➡️ Understanding the horizontal (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mn>0</mn><mi>x</mi></mrow></msub></mrow><annotation encoding="application/x-tex">v_{0x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) and vertical components is <span class="yellow-highlight font-semibold">crucial for analyzing projectile trajectories</span>.<br/>➡️ The calculation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mn>0</mn><mi>x</mi></mrow></msub><mo>=</mo><msub><mi>v</mi><mn>0</mn></msub><mi>cos</mi><mo></mo><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">v_{0x} = v_0 \cos(\theta)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">cos</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span></span></span></span> determines the <span class="yellow-highlight font-semibold">constant horizontal speed</span> throughout the flight.</p>
<p class="mb-4">📸 Video summarized with <a href='https://summarytube.com'>SummaryTube.com</a> on Jan 14, 2026, 06:47 UTC</p>