v = velocity of Tarzan at the bottom as he grabs the vertical vine = 6 m/s
L = length of vine tied to tree at the top = 4.1 m
h = maximum height gained by Tarzan = ?
m = mass of Tarzan
using conservation of energy
maximum potential energy at the top = kinetic energy at the bottom
mgh = (0.5) m v²
gh = (0.5) v²
(9.8) h = (0.5) (6)²
h = 1.84 m
BC = h = height = 1.84 m
AC = length of vine = 4.1 m
AB = AC - BC = 4.1 - 1.84 = 2.26 m
In triangle ABD
Cosθ = AB/AD
Cosθ = 2.26/4.1
Cosθ = 0.55
θ = Cos⁻¹(0.55)
θ = 56.6 deg
