Vertical Motion Under Gravity · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Falling and throwing under gravity

Mathematics · Mechanics · ages 16-17
Name ______________________   Date ____________

  1. A stone is dropped from rest and falls 19.6 m. Take g as 9.8 metres per second squared. How long in seconds does it take?

    Answer: ______________

  2. Upwards is taken as positive. Which value enters the equations for gravity?

    • Positive 9.8 metres per second squared
    • Zero
    • Negative 9.8 metres per second squared

  3. A ball is thrown straight up. What is its velocity at the very top?

    • 9.8 metres per second up
    • 0 metres per second
    • 14 metres per second up

  4. A stone is dropped from rest and falls 122.5 m. Take g = 9.8 m/s squared. How long in seconds does it take?

    Answer: ______________

  5. A ball is thrown upwards at 28 m/s. Take g = 9.8 m/s squared. What is its greatest height in metres?

    Answer: ______________

  6. A ball thrown from a cliff reaches the ground below when t is 4 or negative 1. Which is the landing time?

    • 4 seconds, and negative 1 sits before the throw
    • Negative 1 seconds, and 4 is the extra root
    • Both, because the ball lands twice

  7. A ball thrown from a cliff gives t = 3 or t = negative 0.5 when it reaches the ground below. What does t = negative 0.5 mean?

    • The parabola passed there 0.5 s before the throw, so reject it
    • The ball lands twice
    • The throw never happened
    • The cliff is 0.5 m tall

  8. A ball is thrown upwards at 14 m/s. Take g = 9.8 m/s squared. What is its greatest height in metres?

    Answer: ______________

  9. Ella says the negative root tells when the ball's path, extended back in time, passed that height before the clock started. Is Ella right?

    Circle one:   True   False

  10. A ball thrown up from a cliff gives t = 6 or t = negative 1.5 for reaching the beach below. Max says the ball reaches the beach 1.5 s after the throw. Is Max right?

    Circle one:   True   False

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Answer key

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

Falling and throwing under gravity W1-mt_IgNj9bn14O-s1

  1. 2 · 19.6 equals 4.9 t squared gives t squared 4, so t is 2.
  2. Negative 9.8 metres per second squared · Up is positive, so the downward pull of gravity is negative 9.8.
  3. 0 metres per second · At the top the ball pauses for an instant, so velocity is zero.
  4. 5 · 122.5 = 4.9 t squared gives t squared = 25, so t = 5 s.
  5. 40 · 0 = 784 minus 19.6s gives s = 784 over 19.6 = 40 m.
  6. 4 seconds, and negative 1 sits before the throw · The root after the throw is the landing; the negative root belongs before t is 0.
  7. The parabola passed there 0.5 s before the throw, so reject it · The negative root belongs to the extended mathematics before t = 0, not to the real throw, so the landing time is 3 s.
  8. 10 · At the top v = 0, so 0 = 196 minus 19.6s, giving s = 10 m.
  9. True · The quadratic tracks the whole parabola, including times before t is 0.
  10. False · Max is wrong. Only a positive time comes after the throw, so the ball reaches the beach at 6 s; the negative root belongs to the curve before the throw.
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