Answer:
The maximum height Tarzan and Jane can swing as a fraction of her initial heigh is ⅓h
Explanation:
Let
m = Mass of Tarzan
M = Mass of Jane
Given
M = 2m
To calculate the maximum height Tarzan and Jane can swing, we make use of the potential energy at their initial and final position.
Reason being that;
At both the initial and final position, velocity is 0, so there's no kinetic energy.
And the potential energy remains the same (i.e constant) at any given point in the system.
Using P.E = mgh.
At initial position, PE1 = mgh
At final position, PE2 = (m + M)gH.
Where h and H represent the initial and final heights.
m + M is the new weight after Jane and Tarzan swing
Equating PE1 to PE2
mgh = (m + M)gH
By substituton (M = 2m)
mgh = (m + 2m)gH
mgh = 3mgH
Make H the subject of the formula
H = mgh/3mg
H = ⅓h
Hence, the maximum height Tarzan and Jane can swing as a fraction of her initial heigh is ⅓h
From the question, the new height looks to be about ½ that of Jane's original position; i.e. ½h
The calculated height is smaller than what the cartoon is showing;
We can conclude that the cartoon is wrong.
, while the time is 
, and so
