Motion in a Plane — Formula Sheet

vₓ = v₀ cos θ₀

vy = v₀ sin θ₀ − gt

x = (v₀ cos θ₀) × t

y = (v₀ sin θ₀)t − ½gt²

h = v₀² sin²θ₀ / (2g)

y = x tan θ₀ − g x² / [2(v₀ cos θ₀)²]

v = rω

a_c = v²/r = rω²

F_c = mv²/r = mrω²

T = 2πr/v = 2π/ω

Two essential properties

(i) Constant horizontal velocity (no acceleration horizontally), (ii) Constant downward acceleration equal to g = 9.8 m/s² vertically.

Position at time t

x = v₀cos(θ₀)·t, y = v₀sin(θ₀)·t - ½gt²

Time to maximum height

t = v₀sin(θ₀)/g

Total time of flight

T = 2v₀sin(θ₀)/g

Maximum height

h = (v₀²sin²(θ₀))/(2g)