Jane, looking for tarzan, is running at top speed (5.2 m/s) and grabs a vine hanging 4.5 m vertically from a tall tree in the jungle. how high can she swing upward?

While Jane is running has a kinetic energy, which is Ek = 1/2*m*v^2 where m is mass and v is velocity When she grabs a vine, she is going to change the kinetic energy to potential energy.

We know that potential energy is given by Ep = m*g*h where m is mass, g is gravity constant and h is height

So while running the kinetic energy is Ek = 1/2 * m * 5.2^2 = 13.52*m

Then all that energy is used to swing upward and gain potential energy

Ep = m*g*h = Ek = 13.52*m

m*9.8*h = 13.52*m

h = 13.52/9.8 = 1.38 meters

So Jane will swing 1.38 meters upward