Dropped or thrown: which lands first?

Two balls leave a table edge together, one dropped, one thrown sideways; strobe dots show identical vertical positions. Frame toggle shows a ball dropped from a moving cart: straight down in the cart frame, parabola from the ground.

Pick a horizontal speed so the thrown ball lands 10 m out from a 4.9 m table, and confirm both balls land at the same instant (1.0 s).

A ball thrown horizontally stays in the air longer than one dropped.

• If a is constant, v = v₀ + a t and r = r₀ + v₀ t + ½ a t², as vectors.
• In components: x = x₀ + v₀ₓ t + ½ aₓ t² and y = y₀ + v₀ᵧ t + ½ aᵧ t², with vₓ = v₀ₓ + aₓ t and vᵧ = v₀ᵧ + aᵧ t.
• Motion in a plane with constant acceleration is two independent one-dimensional motions, along x and along y, sharing the same clock t.
• Example: starting at the origin with v₀ = 4.0 î m/s and a = 3.0 ĵ m/s², after 2 s the object is at 8.0 î + 6.0 ĵ m, 10 m from the start, moving at 4.0 î + 6.0 ĵ m/s (about 7.2 m/s).
• The velocity turns steadily towards the direction of a, while the component perpendicular to a never changes.

Teaching this idea? Put the simulation on your own page or LMS with this code.