**Complete part of Question: **What is Jane's (and the vine's) angular speed just before she grabs Tarzan

**Answer:**

Jane's (and the vine's) angular speed just before she grabs Tarzan, **w = 1.267 rad/s**

**Explanation:**

According to the law of energy conservation:

Total change in kinetic energy = Total change in potential energy

Mass of Jane = 60 kg

Mass of the vine = 32 kg

Mass of Tarzan = 72 kg

Height of Tarzan = 5.50 m

Length of the vine = 8.50 m

**Jane's change in gravitational potential energy,**

**Vine's gravitational potential energy,**

**Vine's Kinetic energy :**

**Jane's Kinetic energy:**

3234 + 862.4 = 2167.5w² + 385.33w²

4096.4 = 2552.83w²

w² = 4096.4/2552.83

w² = 1.605

w = √1.605

w = 1.267 rad/s