Tarzan runs at 6 m/s and grabs a vertical vine (negligible mass) 4.1 m long which is tied to a tree at the top. Tarzan swings up.

Determine the maximum height Tarzan will swing up and the angle the vine makes respect to vertical.

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