Vertical motion of bodies

We study vertical motion neglecting air resistance. A body thrown upward with speed υ₀ tends to move uniformly at υ₀ while gravity at the same time pulls it down by gt²/2; so h = υ₀t – gt²/2 and υ = υ₀ – gt. The rise is uniformly decelerated motion; at the top υ = 0, the rise time is tₖ = υ₀/g and the maximum height is h = υ₀²/(2g). Without air resistance the fall time equals the rise time, the body returns to its starting point with the same speed υ₀, and the total flight time is t = 2υ₀/g. A body thrown downward moves with uniform acceleration: υ = υ₀ + gt, h = υ₀t + gt²/2; falling from rest, υ = gt and h = gt²/2. In calculations we take g ≈ 10 m/s² (more precisely 9.8 m/s²); a time-free relation is υ² – υ₀² = ±2gh.