Green iguanas will commonly bask on tall tree branches over the water, and escap

Question

Green iguanas will commonly bask on tall tree branches over the water, and escape predators such as eagles by dropping off the tree and falling into the water. An iguana with a mass of 3 kg is basking on a tree branch 20 meters above the river when it sees a harpy eagle and lets go of the branch. 1 A) What is the velocity of the iguana when it hits the water (neglect aerodynamic forces)? IB) Does this answer depend upon the size of the iguana? IC) What is the kinetic energy of the iguana at the time of impact with the water? ID) If the same iguana drops from a 10 meter high branch, what is the final velocity?

Explanation / Answer

A)At the top, it has a potential energy

U = mgh = 3 x 9.81 x 20 = 588.6 J

When it hita the water, this energy changes into kinetic energy. So:

K = U

1/2 x mv^2 = U

v = sqrt(2U/m) = sqrt(2x588.6/3) = 19.8 m/s

B) yes, because mass determines the potential energy and depending on it kinetic energy and hence velocity is more or less.

C) K = 1/2 x mv^2 = 0.5 x 3 x 19.8^2 = 588.6 J

( this verifies that U =K, i.e law of conservation of energy)

D) in this case, U = 3 x 9.81 x 10 = 294.3 J

Also, K = U

0.5 x 3 x v^2 = 294.3

v = sqrt(294.3 x 2/3) = 14 m/s

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