MONKEY & HUNTER
Aim straight at the falling monkey — the ½gt² cancels and the dart always connects.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
The setup
A hunter aims a dart straight at a monkey hanging in a tree. At the shot, the monkey lets go and drops. Does the dart hit?
Aim
Point the dart along the line of sight, angle θ = tan⁻¹(Y/X). Nothing pushes sideways, so the dart and the monkey share one downward pull: gravity.
Solve
The dart reaches the tree in t = L/v₀. By then both bodies have dropped by the same ½gt², so their aimed paths still meet.
Both fall
Watch both fall. The dart and monkey share the same downward ½gt², so the gap closes exactly to zero.
The verdict
Subtract the heights: Δy = v₀sinθ·t − Y; the gravity terms cancel and the dart arrives before either body reaches ground.