How to solve projectile motion on a TI-84 Plus CE

Worked example: a plane flying level at 150 km/h drops a package from 500 m. How long does it fall, how far forward does it land, and how fast is it going at impact?

The formulas

Sideways speed stays the same: Δx = v₀ₓt. Up and down is free fall with a = −9.8 m/s²: Δy = v₀ᵧt − ½gt², vᵧ = v₀ᵧ − gt. Final speed: v = √(v₀ₓ² + vᵧ²).

By hand

Dropped level, so v₀ᵧ = 0 and Δy = −500 m. Fall time: t = √(2 × 500 / 9.8) = 10.1 s. Speed sideways: 150 km/h ÷ 3.6 = 41.67 m/s, so Δx = 41.67 × 10.10 = 421 m. Then vᵧ = −9.8 × 10.10 = −99.0 m/s and v = √(41.67² + 99.0²) = 107 m/s.

On the calculator with PHYSPRO

Open Motion & projectiles → Fill in: projectile, type only what the problem gives (Δy = −500, v₀ₓ = 150/3.6, v₀ᵧ = 0) and press GRAPH. It finds all 8 unknowns and shows the work for each.

PHYSPRO motion topic with fill-in pages — 1. Pick the fill-in page

Typing the givens — 2. Type what the problem gives

Eight answers with sig figs — 3. Every unknown, with sig figs

Work shown for delta x — 4. The work for any answer

Solve these on your TI-84 Plus CE

PHYSPRO has every formula on this page. Type what the problem gives you and it solves for all the missing values, showing the plug-in line with units and the sig figs. Free.

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