Vektor kelas 10, - Komponen vektor sumbu x dan sumbu y

Main ideas / concepts taught

• The video explains how to find vector components along the X-axis and Y-axis when a vector has a known magnitude and angle relative to the axes.
• It emphasizes interpreting the diagram correctly:
  • X component uses cosine of the angle.
  • Y component uses sine of the angle.
• It includes multiple example problems:
  • A generic vector magnitude/angle case
  • Applications to velocity in east/west (X) and north/south (Y)
  • Problems involving signs (+/−) depending on whether the component points in the positive or negative axis direction

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Method / instructions (vector components)

When a vector has:

• magnitude (a) (or (V))
• angle (\theta) measured from the relevant axis (as shown in the picture)

Use:

• X-axis component: [ a_x = a\cos\theta ]

• Y-axis component: [ a_y = a\sin\theta ]

Notes from the video

• Because these are vector components, you must use the correct sign:
  • Component in the positive axis direction → positive value
  • Component in the negative axis direction → negative value
• When the diagram flips (e.g., vector points left vs. right, up vs. down), the components change sign accordingly.

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Example problems covered

1) Vector magnitude and angle to X-axis

• Given: vector length (a = 20) cm, angle (30^\circ) to the X-axis
• Asked: find (a_x) and (a_y)

Results:

• [ a_x = 20\cos 30^\circ = 20 \cdot \frac{1}{2}\sqrt{3} = 10\sqrt{3} ]

• [ a_y = 20\sin 30^\circ = 20 \cdot \frac{1}{2} = 10 ]

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2) Speed/velocity components (east and north)

• Given: speed (V = 300) km/h, direction angle (\theta = 53^\circ) (between axes as shown)
• Asked: speed components in:
  • East (X-axis)
  • North (Y-axis)

Concept mapping:

• North ↔ Y-axis
• East ↔ X-axis

Results (component rules):

• [ V_x = 300\cos 53^\circ ] Using (\cos 53^\circ = \frac{3}{5}): [ V_x = 300 \cdot \frac{3}{5} = 180\ \text{km/h} ]

• [ V_y = 300\sin 53^\circ ] Using (\sin 53^\circ = \frac{4}{5}): [ V_y = 300 \cdot \frac{4}{5} = 240\ \text{km/h} ]

Also emphasized: Units must stay consistent (km/h).

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3) Second vector with components and sign changes

The final part discusses another vector (labeled like (V_2)) where:

• components must be determined relative to X and Y
• the direction causes negative/positive signs

Key reminders:

• X-component uses cosine
• Y-component uses sine
• The sign depends on whether the component points in the positive or negative direction of the axis

Results stated for (V_2):

• [ V_{2x} = -10\cos 60^\circ = -10 \cdot \frac{1}{2} = -5 ]

• [ V_{2y} = +10\sin 60^\circ = 10 \cdot \frac{\sqrt{3}}{2} = 5\sqrt{3} ]

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Sources / speakers featured

• No identifiable named speakers are mentioned in the subtitle text.
• Primary speaker: an unnamed instructor/teacher (implied by the teaching narration and “Bismillahirrahmanirrahim” opening and step-by-step explanations).