Question

Hey guys! I have a fairly easy Physics question, or so it seems, I'm just not sure how to get started on this. Please take a look at the comments; the wording is rather long.

Answer 1

Because of your concern that incorrect science is being taught to children when they watch cartoons on TV, you have joined a committee which is reviewing a new cartoon version of Tarzan.
In this episode, Tarzan is on the ground in front of a herd of stampeding elephants. Just in time, Jane, who is up in a tall tree, sees him. She grabs a convenient vine and swings towards Tarzan,who has twice her mass, to save him. Luckily, the lowest point of her swing is just where Tarzan is
standing. When she reaches him, he grabs her and the vine. They both continue to swing to safety over the elephants up to a height which looks to be about 1/2 that of Jane's original position.

To decide if you going to approve this cartoon, calculate the maximum height Tarzan and Jane can swing as a fraction of her initial height.

Answer 2

Look at this diagram where Jane starts at height \(h_i\), and Tarzan is standing at h=0 and their new height is unknown. The easiest way to calculate this is in terms of potential energy.

At the initial height \(\sf h_i\) , Jane has potential energy \(\sf PE=m_{J}*g*h_i\)

Notice \(\sf m_J\) is the mass of J alone

Assuming that there is no energy loss when J picks up T, they will reach the height according to the new m of both persons, \(\sf m_{J+T}\).

Now the new height is: \(\sf PE=m_{J+T}*g*h_{new}\rightarrow h_{new}=\dfrac{PE }{m_{J+T}*g}\)

Their combined weight is 3 times the original: \(\sf m_{J+T}=3m_J\)

\( \sf h_{new}=\dfrac{PE }{3m_J*g}\)

we can plug in the value of PE from the the first equation to eliminate some constants.

\( \sf h_{new}=\dfrac{\cancel m_{J}*\cancel g*h_i}{3\cancel m_J*\cancel g}=\dfrac {h_i}{3}\)

So the height they achieve together is 1/3 of the original height.