Question

Jane, looking for Tarzan, is running at top speed (4.9 m/s) and grabs a vine hanging 3.6 m vertically from a tall tree in the jungle. If air resistance is neglected, how high can she swing upward? Hint: use the conservation of energy.

Answer 1

To solve this problem we will apply the energy conservation equations, for which we have that the potential energy accumulated at a certain height is equivalent to the kinetic energy in the body and that generates a certain movement on it. Kinetic energy can be described as

`KE = (1)/(2) mv^2`

Where,

m = mass

v = Velocity

At the same time,

`PE = mgh`

Here,

h = Height

g = Gravitational acceleration

As PE = KE, we have that,

`mgh = (1)/(2) mv^2 \\h = (v^2)/(2g)\\h = (4.9^2)/(2(9.8))\\h = 1.225m`

Therefore she can swing upward around of 1.225m