JEE/NEET Physics · Motion in a Straight Line series · Part 4 of 6 · All parts →
- In free fall (air ignored) everything accelerates at g ≈ 9.8 m/s² downward — mass doesn’t matter
- The three equations survive with a = −g (up + convention) or +g (down + convention)
- Up-and-down trips are symmetric: rise time = fall time; launch speed = landing speed
- Maximum height: v = 0 there → H = u²/2g
- Signs are everything: pick up as + once, then g is −, and landings below the start have negative s
Drop a coin and a key together: they hit the ground together. Heavy or light, everything falls with the same acceleration — gravity’s great democracy. Part 4 of the Motion in a Straight Line series.
- Free fall: the mass surprise
- Throwing up: the symmetric trip
- Maximum height and time of flight
- The sign convention that saves you
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Free Fall: The Mass Surprise
Gravity pulls harder on heavier things (mg), but heavier things are also harder to accelerate (ma with bigger m) — and the two effects cancel exactly: a = g for everyone. A feather loses only because air drag cheats; in a vacuum it keeps pace with a hammer (Apollo 15 proved it on the Moon).
Throwing Up: The Symmetric Trip
Toss a ball up at u. It decelerates at g, stops for an instant at the top (v = 0, but a is STILL g — gravity never takes a break), then falls back symmetrically: rise time = fall time = u/g, landing speed = launch speed. The top is a pause, not a hover.
Maximum Height and Time of Flight
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| g | free-fall acceleration near Earth’s surface | ≈ 9.8 m/s², always DOWN (sign is yours to set) |
| H | maximum height above launch | m |
| u | launch (initial) speed upward | m/s |
The Sign Convention That Saves You
Take UP as + (the usual choice for tosses). Then a = −9.8 always, up-velocities start positive and decay, and any landing BELOW the launch point has s negative. All three golden equations then work unchanged. Most vertical-motion errors are sign errors, not physics errors.
Solved Examples
v = gt = 30 m/s; s = ½gt² = 45 m.
✔
Answer: 30 m/s; 45 m
H = u²/2g = 400/20 = 20 m; t_up = u/g = 2 s; full flight = 4 s.
Landing speed = 20 m/s again — perfect symmetry. ✔
Answer: H = 20 m; 4 s flight
Down +: u = −15, a = +10, s = +20: 20 = −15t + 5t² → t² − 3t − 4 = 0 → t = 4 s (reject −1).
4 s — the quadratic’s negative root is physics asking to be thrown backwards in time. ✔
Answer: 4 s
- Heavy falls faster. No — mass cancels; only air resistance (ignored here) breaks the tie.
- v = 0 at the top means a = 0. Wrong — velocity pauses, acceleration stays a full g downward the whole flight.
- Using +g while calling up positive. With up +, g enters every equation as −9.8; mixing signs flips answers silently.
- Forgetting displacement sign below launch. Ball landing under the start point: s is negative (up + convention) — the equation knows where the ground is only if you tell it.
This Physics in Your Daily Life
- Water from a tap ‘beads’ into droplets that accelerate as they fall — the widening spacing between drops is a live ½gt² graph.
- Catch a high ball and it stings more than a low one — landing speed grows with fall height (√(2gh)): your hands are doing v² = u² + 2as.
- Amusement drop-towers are engineered near-g falls: the stomach-lift IS your body briefly in free fall, everything falling together.
- Cricket fielders’ high catches — they start moving BEFORE the ball peaks, because rise time = fall time tells them the schedule.
- Rainbows of fountains — designers tune jet speed u to reach height u²/2g: every fountain arc is this card in water.
Galileo’s legend: drop a cannonball and a musket ball from the Tower of Pisa — they land together. Gravity writes a bigger pull on the cannonball, but inertia writes a bigger refusal on it too, in exactly the same proportion. The two cancellations are perfect; the universe doesn’t check your weight before accelerating you.
Numbers: g = 9.8 m/s² for all. After 1 s: 9.8 m/s; after 2 s: 19.6; after 3 s: 29.4 — every falling object runs this exact velocity schedule, stone or boulder. Height fallen: 4.9, 19.6, 44.1 m — one timetable for the whole planet.
Draw v-t for a toss: a straight line tilting down through zero — up-velocity bleeding away, zero at the top (a single point, not a shelf), then negative growing. The SAME straight line covers rise and fall: one slope (−g), one picture, symmetric either side of the zero-crossing.
Practice set (answers hidden — try first)
(NEET-level) Dropped from rest, speed after 2 s (g=10):
(JEE Main-level) u = 30 m/s up. Time back to the hand:
(NEET-level) Height reached at u = 20 (g=10):
(Concept) At the highest point of a throw:
(JEE Main-level) Fall from 45 m: time (g=10) =
- free fall: a = g for ALL masses
- up + convention: a = −9.8 throughout
- top of flight: v = 0, a = g still
- H = u²/2g, T_flight = 2u/g (same level)
- symmetry: rise = fall, launch speed = landing speed
- 🔁 all masses fall at g
- 🔁 v = 0 but a = g at the top
- 🔁 H = u²/2g · T = 2u/g
- 🧠 Chant: ‘gravity never rests — even at the top’.
- 🧠 Symmetry: ‘up-mirror is down-mirror’.
- 🧠 g ≈ 10 for quick maths, 9.8 for accuracy.
- 🏠 Daily: tap-water drop spacing = the ½gt² graph live.
- 🏠 Daily: fielders run early because rise time = fall time.
Quick revision
- In free fall (air ignored) everything accelerates at g ≈ 9.8 m/s² downward — mass doesn’t matter
- The three equations survive with a = −g (up + convention) or +g (down + convention)
- Up-and-down trips are symmetric: rise time = fall time; launch speed = landing speed
- Maximum height: v = 0 there → H = u²/2g
- Signs are everything: pick up as + once, then g is −, and landings below the start have negative s
- Free fall: the mass surprise
Have a doubt on this topic?
