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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?

User Urema
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1 Answer

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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
User Bismark
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