Resolving Vectors into Components · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Resolving vectors into parts

Science · Forces & Motion · ages 16-17
Name ______________________   Date ____________

  1. A vector has size A at angle theta from the x axis. What is its x component?

    • A times sin theta
    • A times tan theta
    • A times cos theta

  2. A velocity of 20 metres per second points at 30 degrees above the x axis. What is its vertical part in metres per second?

    Answer: ______________

  3. What does resolving a vector mean?

    • Splitting it into perpendicular parts
    • Adding two vectors into one longer arrow
    • Measuring its size with a ruler

  4. Which axes shorten a problem about motion along a slope?

    • Always north and east
    • Along and across the slope
    • Along the weight arrow only

  5. Three pulls share x parts 3, negative 3, 0 and y parts 0, 0, 4. What is the resultant?

    • 4 N north
    • 4 N east
    • 10 N north

  6. Kim says pointing the axes a different way changes the physics of the motion. Is Kim right?

    Circle one:   True   False

  7. Sid measures the angle from the y axis but still writes x as A times cos. Is Sid right?

    • No, the x part takes sine
    • Yes, x always takes cosine
    • No, resolving there needs tan only

  8. Three forces have (x, y) parts (5, 0), (negative 2, 0) and (0, 4). What is the resultant as size and angle?

    • 7 at 45 degrees above east
    • 5 at 53 degrees above east
    • 5 at 37 degrees above east
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Resolving vectors into parts W1-mt_tc698unGJG-s1

  1. A times cos theta · Cosine sits beside the angle, so the beside part, x, takes cosine.
  2. 10 · The vertical part is 20 times sin 30, which is 20 times 0.5.
  3. Splitting it into perpendicular parts · Each part then acts alone along its own axis.
  4. Along and across the slope · Aligned axes kill the most terms, leaving weight as the only split.
  5. 4 N north · Total x is 0 and total y is 4, so the resultant is 4 straight north.
  6. False · Axes are your choice: the physics stays put while the arithmetic changes.
  7. No, the x part takes sine · Cosine sits beside the angle, which is the y side here, so x takes sine.
  8. 5 at 53 degrees above east · Totals are x 3 and y 4, so size 5, and tan is 4 over 3, about 53 degrees.
Worksheet · LightMySky