Projectile Motion · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Two lives of a flying ball

Mathematics · Mechanics · ages 17-18
Name ______________________   Date ____________

  1. A projectile's horizontal component is 12 m/s and cos(theta) = 0.6. What is the launch speed in m/s?

    Answer: ______________

  2. A projectile launches at 10 m/s at 45 degrees above the horizontal. The velocity triangle is isosceles, so its two legs are equal. Which statement about the initial components is true?

    • The horizontal component is larger
    • The vertical component is larger
    • They are equal

  3. A ball launches at 25 m/s with cos(theta) = 0.8 and sin(theta) = 0.6. What are its components?

    • 20 m/s horizontal and 15 m/s vertical
    • 15 m/s horizontal and 20 m/s vertical
    • 25 m/s in both directions

  4. The standard projectile model ignores air resistance.

    Circle one:   True   False

  5. A ball rolls off a 45 m platform horizontally at 15 m/s. Take g = 10. How far from the base does it land, in metres?

    Answer: ______________

  6. With no air resistance, horizontal velocity stays constant through the flight.

    Circle one:   True   False

  7. A projectile launches upward from a cliff and lands below the launch height. A student uses 2uy/g for the flight time. What is wrong with this?

    • 2uy/g only applies when landing at launch height
    • 2uy/g always works for any landing height
    • 2uy/g gives the time to apex, not the flight time

  8. At the apex of a projectile's flight, the acceleration is zero. True or false?

    Circle one:   True   False

  9. A ball launches from ground level at 25 m/s with cos(theta) = 0.8 and sin(theta) = 0.6. Take g = 10. It lands at launch height. What is its range in metres?

    Answer: ______________

  10. A projectile has ux = 12 m/s and uy = 16 m/s. Take g = 10. What is its speed after 1 s? Give your answer to one decimal place.

    • 20.0 m/s
    • 13.4 m/s
    • 28.0 m/s
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Answer key

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

Two lives of a flying ball W1-mt_O1C-QxCSJN-s1

  1. 20 · ux = u cos(theta), so 12 = u × 0.6, giving u = 12 ÷ 0.6 = 20 m/s.
  2. They are equal · At 45 degrees the velocity triangle is isosceles, so ux = uy. Both are 10 cos(45°) ≈ 7.07 m/s.
  3. 20 m/s horizontal and 15 m/s vertical · Multiply 25 by 0.8 and by 0.6.
  4. True · Leaving drag out keeps horizontal velocity constant and the maths clean.
  5. 45 · The fall time is √(2 × 45/10) = 3 s. The range is 15 × 3 = 45 m.
  6. True · No horizontal force means no horizontal acceleration.
  7. 2uy/g only applies when landing at launch height · 2uy/g assumes the landing returns to the launch height. A lower landing needs the vertical position equation solved as a quadratic.
  8. False · At the apex vy = 0 but the downward acceleration g remains. Acceleration is never zero in the gravity-only model.
  9. 60 · The vertical component is 15 m/s, so the flight time is 2 times 15/10 = 3 s. The range is 20 times 3 = 60 m.
  10. 13.4 m/s · vy = 16 - 10 × 1 = 6 m/s. Speed = √(12² + 6²) = √180 ≈ 13.4 m/s.
Worksheet · LightMySky