Tarzan (mass 100 kg) holds one end of an ideal vine (infinitely strong, completely flexible, but having zero mass). The vine runs horizontally to the edge of a cliff, then vertically to where Jane (mass 50 kg – she went on a diet since question #13) is hanging on, above a river filled with hungry crocodiles. A sudden sleet storm has removed all friction. Assuming that Tarzan holds on, what is his acceleration towards the cliff edge?

Question

Tarzan (mass 100 kg) holds one end of an ideal vine (infinitely strong, completely flexible, but having zero mass). The vine runs horizontally to the edge of a cliff, then vertically to where Jane (mass 50 kg – she went on a diet since question #13) is hanging on, above a river filled with hungry crocodiles. A sudden sleet storm has removed all friction. Assuming that Tarzan holds on, what is his acceleration towards the cliff edge?

Answer 1

To determine Tarzan's acceleration towards the cliff edge, we need to consider the forces acting on the system.

First, let's calculate the total force acting on the system. The system consists of Tarzan, Jane, and the vine, so the total mass of the system is the sum of their masses: 100 kg + 50 kg = 150 kg.

Now, let's analyze the forces:

1. Tension in the vine: Since the vine is ideal, it has zero mass and exerts a tension force only. The tension in the vine acts horizontally towards the cliff edge.

2. Gravitational force: Both Tarzan and Jane are subject to the force of gravity, which acts vertically downwards.

Since there is no friction, the tension force in the vine is the only horizontal force acting on the system. According to Newton's second law, the net force on the system is equal to the mass of the system multiplied by its acceleration.

Therefore, we can set up the following equation:

Net force = Mass × Acceleration

The net force is equal to the tension force in the vine, which is the only horizontal force in this case.

The mass of the system is 150 kg, and we'll denote the acceleration as "a".

So we have:

Tension force = Mass × Acceleration
Tension force = 150 kg × a

Now, let's consider the vertical forces:

Tarzan's weight = 100 kg × g (where g is the acceleration due to gravity, approximately 9.8 m/s^2)
Jane's weight = 50 kg × g

Since the vine is flexible and massless, the tension in the vine acts as a balancing force against the vertical forces.

Therefore, we can set up the following equation:

Tension force = Tarzan's weight + Jane's weight

150 kg × a = 100 kg × g + 50 kg × g

Simplifying the equation:

150 kg × a = 150 kg × g

Now, we can cancel out the mass terms:

a = g

Hence, Tarzan's acceleration towards the cliff edge is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.