Presets
Parameters
Live readouts
Model check
The science
Branch as a springboard
A colobus monkey bends a branch with its weight, then lets it spring back. If a fraction η of the elastic energy ½ k x² becomes kinetic energy, the take-off speed is v0 = √(η k x² / m). After that it is a projectile: x = v0 cosθ · t, y = v0 sinθ · t - ½ g t². For a target a height H above the launch (negative = below) the landing distance is x = v0 cosθ (v0 sinθ + √(v0² sin²θ - 2 g H)) / g; on level ground the best angle is 45 degrees, and for a lower target it is smaller.
What this view adds
A side view of the leap with the no-drag and drag trajectories, the landing zone on the target branch, a landing-distance-versus-angle curve (analytic against RK4 with drag), and height and speed against time.
Simplifications
Point mass, a constant efficiency η = 0.8 for the branch (real branches are damped and move while the animal pushes), a fixed tucked-body drag area, no rotation or limb-swing, a fixed 1.6 m landing zone, and no moment when the hands grab the branch. Numbers are plausible for a leap of 10 m but are not measured primate data.