Question

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 1

Step 1: Using energy conservation find speed of Jane just as she at the bottom of swing:

KEi + PEi = KEf + PEf

KEi = 0, since Jane started from rest

PEi = m*g*h, (Assuming reference point is where Tarzan is standing and Jane is 'h' height above Tarzan)

KEf = (1/2)*m*V^2

PEf = 0, since potential energy is zero at reference point

So,

0 + m*g*h = (1/2)*m*V^2 + )

V = sqrt (2*g*h)

Step 2: Since there is no external force applied on the system of Jane-Tarzan, So using momentum conservation before and after collision:

Pi = Pf

Since both Jane and tarzan move together after collision, So this is an example of completely inelastic colliision

m1*V1 + m2*V2 = (m1 + m2)*V

m1 = mass of jane = m, m2 = mass of Tarzan = 2*m

V1 = Initial speed of jane just before collision = sqrt (2*g*h)

V2 = Initial speed of tarzan just before collision = 0

V = final speed of both after collision = ?

V = (m1*V1 + m2*V2)/(m1 + m2)

V = (m*sqrt (2*g*h) + 2m*0)/(m + 2m)

V = (1/3)*sqrt (2*g*h)

Step 3: Now again apply energy conservation after collision:

KEi + PEi = KEf + PEf

KEi = (1/2)(m1 + m2)*V^2 = (1/2)*(m + 2m)*((1/3)*sqrt (2*g*h))^2

KEi = (3*m*2*g*h/(2*9)) = m*g*h/3

PEi = Initial PE of both at reference point = 0 J

KEf = 0, since at max height speed of both will be zero.

PEf = (m1 + m2)*g*H_max = (m + 2m)*g*H_max

PEf = 3m*g*H_max

So

m*g*h/3 + 0 = 0 + 3*m*g*H_max

H_max = h/9 (So Jane can only jump (1/9) of her initial height)

Now since in the cartoon Jane jumps with Tarzan at about half of her initial height, So Cartoon is teaching incorrect science.

Let me know if you've any query.