What is tarzan's speed vf just before he reaches jane? express your answer in meters per second to two significant figures?

Before swinging, T has only potential energy, (no speed)

Ui = mgh

Where h is the vertical displacement of T

From the laws of geometry,

cos45 = (L-h) / L

cos45 = 1-h/L

h/L = 1-cos45

h = L (1-cos45)

Therefore

Ui = mgL (1-cos45)

Proceeding the same way,

Twill raise to aheight of h' due to swing

h' = L (1-cos30)

The PE of T after swing is

Uf = mgh'

Uf = mgL (1-cos30)

Along with the PE, T has some kinetic energy results due to the moment.

Tf = 0.5*mv^2

According to the law of conservation of energy,

Ui = Uf+Tf

mgL (1-cos45) = mgL (1-cos30) + 0.5*mv^2

gL (co30-cos45) = 0.5*v^2

9.8*20 * (co30-cos45) = 0.5*V^2

v = 7.89 m/s

The speed f T after swing is 7.89 m/s