Fleas have remarkable jumping ability. A 0.60 mg flea, jumping straight up, would reach a height of 35 cm if there were no air resistance. In reality, air resistance limits the height to 20

**Answer 1**

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A

find the flea’s initial V

Vf^2 = Vi^2 + 2 g d

Vf at top is 0

0 = Vi^2 + 2 (-9.8) (0.35)

Vi^2 = 6.86

Vi = 2.62 m/s

find KE

KE = 1/2 m v^2 = 1/2 (0.60E-6 kg) (2.62 m/s)^2 = 2.06E-6 J

B

find PE

GPE = m g h = 0.60E-6 kg (9..8) (0.20 m) = 1.176E-6 J

find the fraction of KE

PE / KE = 1.176E-6 / 2.06E-6 = 0.57 or 57%

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**Answer 2**

That’s 0.6 of 1 milligram, which is 0.6 of 1/1000th. kg.

0.6mg = 0.0006 kg.

20cm = 0.2m.

35cm = 0.35m.

Initial V = sqrt.(2gh) = sqrt.(19.6 x 0.35) = 2.62m/sec.

a) KE = 1/2 (mv^2) = 1/2 (0.0006 x 2.62^2) = 0.002059 J. (2.059e-3)

b) PE = (mgh) = (0.006 x 9.8 x 0.2) = 0.001176 J. (1.176e-3)

c) (0.001176/0.002059) = 0.57 = 57/100ths