Question

a 55.0-kg scientist roping through the top of a tree in the jungle sees a lion about to attack a tiny antelope. she quickly swings down from her 12.0-m-high perch and grabs the antelope (21.0 kg) as she swings. they barely swing back up to a tree limb out of reach of the lion. how high is this tree limb?

Answer 1

The height of the tree limb is 6.28m.

Mass of scientist = M = 55 Kg

Mass of antelope = m = 21 Kg

Acceleration due to gravity = g = 9.8 m/s²

Initial height = h = 12 m

Speed = v

Using the law of Energy Conservation;

= Total Energy = Kinetic Energy + Potential Energy

= E = (1/2)mv² + mgh

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 = (1/2)mv²

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 = mgh

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

= (1/2)mv² = mgh

Now,

Equating both the heights,

= h₂ = ( M / M+m ) X h₁

= h₂ = (55 / 55 +21) X 12

= h₂ = 6.28 m

To know more about Energy Conservation:

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