projectile motion formulas

flight time

2(-Vo sinθ) /g

range Δx (displacement when launched)

(Vo^2 sin2θ) /g OR Vo(cosθ)t

x

hyp (cosθ)

y

hyp (sinθ)

Δx (from rest)

Vox(t)

Vfx (from rest)

Vox

a (from rest)

0

Δy (from rest)

1/2gt^2

t (from rest)

√2Δy /g

Voy (from rest)

0

Vfy (from rest)

gt

Vfy^2 (from rest)

2gΔy

g (from rest)

-10m/s^2

Vfx (launched)

Vo(cosθ) (same)

Δy (launched)

Vo(sinθ) + 1/2gt^2

Vfy (launched)

Vo(sinθ) + gt

Vfy^2 (launched)

Vo^2(sinθ)^2 + 2gΔy

Vo (straight up)

Vy top + 1/2gt

Δy max (straight up)

Vo(t/2) + 1/2g(t/2)^2

Vf (OG)

Vo + at

Δx (OG)

Vo(t) + 1/2at^2 OR ((Vf+Vo)/2)(t)

Vf^2 (OG)

Vo^2(t) + 2aΔx

Δy max (launched)

Vo(sinθ)t/2 + 1/2g(t/2)^2