NapkinCalc

Physics 1 — Motion & Energy

Free fall

continues from lesson 1 — values defined earlier in the course stay live here

ELI5: drop anything and gravity pulls with a constant acceleration g ≈ 9.81 m/s² — so the same two equations apply, starting from v₀ = 0. A surprise: the fall time grows with the square root of height, so dropping from 4× the height takes only 2× as long.

g:=9.81m/s2g := 9.81 m/s^2 = 9.81 m / s^2 gravitational acceleration
h0:=45mh_{0} := 45 m = 45 m drop height
tfall:=sqrt(2∗h0/g)t_{fall} := sqrt(2 * h_{0} / g) = 3.0289 s time to hit the ground
vimpact:=g∗tfallv_{impact} := g * t_{fall} = 29.714 m / s impact speed

Real-world hook: "count the seconds" to estimate a cliff's height, the physics of a bungee jump, and why a fall from twice the height hurts far more than twice as much (impact speed grows with √height, energy with height).

Try it yourself: how long does an object take to fall from 20 m? (t = √(2h/g).)

tyou:=sqrt(2∗20m/g)t_{you} := sqrt(2 * 20 m / g) = 2.0193 s ✏️ Your turn: compute the fall time √(2·20 m / g). Answer in seconds.
✓ pass abs(tyou−sqrt(2∗20m/g))<0.01sabs(t_{you} - sqrt(2 * 20 m / g)) < 0.01 s green when your fall time is correct