For its size, the common flea is one of the most accomplished jumpers in the ani

Question

For its size, the common flea is one of the most accomplished jumpers in the animal world. A 1.70 mm -long, 0.550 mg critter can reach a height of 20.0 cm in a single leap. part A: Neglecting air drag, what is the takeoff speed of such a flea? Part B: Calculate the kinetic energy of this flea at takeoff and its kinetic energy per kilogram of mass. Part D:If a 73.0 kg , 1.70 m -tall human could jump to the same height compared with his length as the flea jumps compared with its length, how high could he jump, and what takeoff speed would he need? part F: In fact, most humans can jump no more than 60.0 cm from a crouched start. What is the kinetic energy per kilogram of mass at takeoff for such a 73.0 kg person?

Explanation / Answer

Ans:A.
KE=PE; PE=mgh; KE=.5mv2
v=sqrt(2gh)
v= sqrt ( 2 x 9.8 m/s2 x 20cm x (1 m / 100 cm) =1.98 m/s
B.
KE = .5mv2
= .5 x .55 mg (1 kg / 1,000,000 mg) (1.98 m/s)2
= 10.78x 10 -7

D.
ratio/proportion fomula
d(human)/1.7m = 20cm (1m/100cm) / 1.7 mm (1m/1,000 mm)
d(human) = 200 m

v=sqrt (2gh)
= sqrt (2 x 9.8 m/s2 x 200 m )
= 62.60 m/s
F.
PE=KE =mgh/m
=gh
=9.8 m/s2 x 60 cm (1 m /100 cm)
= 5.88 J/kg

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