# How Does Tarzan Accelerate Towards the Cliff in a Frictionless Scenario?

• Tensaiga
In summary, Tarzan (100kg) holds one end of an ideal vine while Jane (50kg) is hanging on the other end above a river. Due to a sudden sleet storm, all friction is removed and Tarzan is accelerating horizontally towards the end of the cliff. Using Newton's 2nd law and setting up free body diagrams for both Tarzan and Jane, we can solve for the acceleration, which is found to be 3.26m/s^2. The tension in the rope is calculated to be 326.67N.
Tensaiga
Hello, i can't seem to figure this out...i need some help.

Tarzan (mass 100kg) 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 50kg) is hanging on, above a river. A sudden sleet storm has removed all friction, assuming that Tarzan hangs on, what is his accerleration towards the end of the cliff?

umm, i have no thoughts on this one, how can i solve this without knowing any other variables expect their masses??

Thanks

Last edited:
Apply Newton's 2nd law to both Tarzan and Jane. You'll get two equations, which you can solve together to find the acceleration.

Hint: Since they are connected by a rope, Tarzan's horizontal acceleration will equal Jane's vertical acceleration.

HUH?? sorry, i don't get it...but isn't Jane attached to the cliff? i mean she's hanging on the edge of the cliff? Isn't she at rest?

Tensaiga said:
HUH?? sorry, i don't get it...but isn't Jane attached to the cliff? i mean she's hanging on the edge of the cliff? Isn't she at rest?
I think you misunderstood the question. She is only holding to the vine. And she is accelerating (in fact, the magnitude of her acceleration is the same as the magnitude of the acceleration of Tarzan). Do as Doc Al suggested: set up free body diagrams for Tarzan and Jane and then solve (actually, it's possible here to combine the two in a single equation and do everything in one step but I think it hides a bit the physics.)

So set up a FBD for Tarzan, one for Jane, identify the forces, setp up Newton's second law, see how the acceleration of Tarzan is related to the acceleration of Jane and you will have two eqs for two unknowns (being the tension in the rope and the acceleration).

umm, sorry i can't even figure out how to draw the FBD... how are they connected ? Tarzan is holding the vine, and so is Jane? then why did he had to run horizontally? I'm lost...

Code:
Think Tug-o-War, Tarzan-----CliffEdge\
|
|
|
|
|
Jane

~~~~River~~~~

Tensaiga said:
HUH?? sorry, i don't get it...but isn't Jane attached to the cliff? i mean she's hanging on the edge of the cliff? Isn't she at rest?
Gravity is pulling Jane (50 kg) down. The tension in the rope simply couples the force and mass of Jane (50 kg) to Tarzan (100 kg).

So what is the force acting on Jane? Think of weight.

What mass is being accelerated by the force on Jane?

Another way to look at it - Tarzan's mass is resisting the acceleration of Jane. Also since the two are coupled, Jane and Tarzan must be accelerating at the same rate, although Jane is accelerating downward and Tarzan is accelerating horizontally.

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ohhhh i get it thank you very much with that diagram.
the tensional force is the force pulling down Tarzan, thus the two equations are:

a = T/m and a = (mg-T)/m

plug in the variables:
T/100 = (50*98-T)/50
T = 326.67N

Then accleration must be 3.26m/s^2

Thank YOU ALL

## 1. How is it possible for Tarzan to swing through the jungle without a vine breaking?

This is possible due to the conservation of angular momentum. As Tarzan swings, he gains angular momentum and the vines stretch, storing potential energy. When he reaches the end of the swing, the vines release this potential energy, propelling him forward. This process is repeated and the vines are strong enough to withstand this force.

## 2. How does Tarzan change direction while swinging?

Tarzan is able to change direction by changing the angle at which he releases the vine. By releasing the vine at a specific angle, he can alter his trajectory and change direction.

## 3. How fast is Tarzan swinging through the jungle?

The speed at which Tarzan swings depends on various factors such as the length and strength of the vine, the angle at which he starts swinging, and his body weight. It is difficult to determine an exact speed without specific measurements, but it is estimated that he could reach speeds of up to 25 miles per hour.

## 4. Is it physically possible for Tarzan to swing from vine to vine without touching the ground?

Yes, it is possible for Tarzan to swing from vine to vine without touching the ground. As explained earlier, the vines are able to store and release potential energy, allowing Tarzan to continue swinging without interruption. However, this would require precise timing, strength, and agility from Tarzan.

## 5. Could Jane also swing through the jungle like Tarzan?

Yes, Jane could also swing through the jungle like Tarzan as long as she has the necessary strength and agility. However, it is important to note that the strength and length of the vines may vary, making it more challenging for Jane to swing with the same ease as Tarzan.

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