Eleventh Grade · Science · week 6

Free Fall

Apply the kinematic equations to free-fall motion using a constant acceleration of 9.8 m/s^2 due to gravity.

Near Earth's surface, any object moving through the air under gravity alone (ignoring air resistance) accelerates downward at a constant 9.8 m/s^2 -- a value physicists call "g." This is just a special case of last week's constant-acceleration kinematics, with a = -9.8 m/s^2 if we choose "up" as the positive direction, whether the object is rising, falling, or momentarily paused at the very top of its path. Famously, this acceleration does not depend on mass: a bowling ball and a tennis ball, dropped together with no air resistance, hit the ground at the exact same instant.

Free fall has a useful symmetry when an object returns to its starting height: the time spent rising equals the time spent falling, and the speed at any given height is the same on the way up as on the way down (same magnitude, opposite direction). At the very peak of a toss straight up, velocity is momentarily zero -- but acceleration is NOT zero; gravity never stops pulling, which is exactly why the object does not stay at the peak.

📋 For the teacher
Teach it (10–15 min):
  • If you have any two objects of very different weight (a coin and a crumpled piece of paper work poorly because of air resistance -- try a coin and a slightly heavier coin, or two balls of different size), drop them together from the same height and watch them land together. It is the single most convincing free-fall demonstration there is.
  • Narrate the ball-toss example as a story: "leaving your hand fast, slowing the whole way up, a heartbeat of zero speed at the very top, then speeding back up the whole way down" -- the constant acceleration underneath all four phases is the one idea to land.
  • Use a phone's slow-motion video feature to film a dropped object next to a ruler taped to a wall, then step through the frames together to see the object cover more distance each successive fraction of a second -- visual proof that a is constant while v keeps growing.
  • When solving, keep asking "which direction is positive in THIS problem?" out loud -- consistency of sign convention prevents the majority of free-fall errors.
Talk about it:
  • Why do a heavy object and a light object fall at the same rate when air resistance is ignored?
  • Why is the time going up equal to the time coming down, for an object that returns to its starting height?
  • What is true about a ball's velocity and its acceleration at the very top of its path -- are they ever both zero at once?

Mastery looks like: They apply the kinematic equations to a free-fall scenario with a = -9.8 m/s^2, correctly finding time, height, or speed as needed.

Common stumbles: Believing heavier objects fall faster; assuming that because velocity is zero at the peak, acceleration must be zero there too.

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Records attendance + 15 min of Science for this learner.
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