Question

Jane, looking for tarzan, is running at top speed (6.8 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. how high can she swing upward?

Answer 1

Jane's mechanical energy at any time is

`E=U+K`
where
`U=mgh` is the potential energy, while
`K= (1)/(2) mv^2` is the kinetic energy.

Initially, Jane is on the ground, so the altitude is h=0 and the potential energy is zero: U=0. She's running with speed v, so she has kinetic energy only:

`E=K= (1)/(2) mv^2`
Then she grabs the vine, and when she reaches the maximum height h, her speed is zero: v=0, and so the kinetic energy becomes zero: K=0. So now her mechanical energy is just potential energy:

`E=U=mgh`

But E must be conserved, so the initial kinetic energy must be equal to the final potential energy:

`(1)/(2)mv^2=mgh`
from which we can find h, the maximum height Jane can reach:

`h= (v^2)/(2g)= ((6.8 m/s)^2)/(2\cdot 9.81 m/s^2)=2.36 m`