Fleas have remarkable jumping ability. A 0.45 mgflea, jumping straight up, would

Question

Fleas have remarkable jumping ability. A 0.45 mgflea, jumping straight up, would reach a height of 30 cm if there were no air resistance. In reality, air resistance limits the height to 20 cm .

Part A

What is the flea's kinetic energy as it leaves the ground?

Part B

At its highest point, what fraction of the initial kinetic energy has been converted to potential energy?

Fleas have remarkable jumping ability. A 0.45 mgflea, jumping straight up, would reach a height of 30 cm if there were no air resistance. In reality, air resistance limits the height to 20 cm .

Part A

What is the flea's kinetic energy as it leaves the ground?

Part B

At its highest point, what fraction of the initial kinetic energy has been converted to potential energy?

Explanation / Answer

So, first lets determine the maximum amount of energy in the system which is PE = mgh (at 30cm or .3m), also a 0.45 mg flea weighs 4.5*10^-7 kg. so PE = (4.5E-7)(9.8)(0.3) = 1.323 E-6 J.
The kinetic energy as it leaves the ground is 1.323E-6 because Etotal = PE + KE, and on the ground h = 0 mgh = 0 and Etotal = KE

a) 1.323E-6 joules
b) I have some confusion as to what the highest point is, so Ill solve it both ways.

assuming the highest point is 30 cm:

also at the highest point the velocity = 0. so KEhighest = 1/2 mv2 = 0. Therefore 100% of the KE.

PE = 1.323 E-6 J

assuming the highest point is 20 cm:

Ke here also = 0 because v = 0.

PE = (4.5e-7)(9.8)(.2) = 8.82e-7 which is 50% of the initial KE.

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