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 2.50mm -long, 0.510mg critter can reach a height of 19.0cm in a single leap. Found the takeoff speed of this flea is 1.93 m/s. A) Calculate the kinetic energy of this flea at takeoff AND its kinetic energy per kilogram of mass? B) If a 80.0kg , 1.70m -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? C)In fact, most humans can jump no more than 60.0 from a crouched start. What is the kinetic energy per kilogram of mass at takeoff for such a 80.0person?

Explanation / Answer

l = 2.50 mm = 0.0025 m; L = 1.7 m
m = 0.510 mg = 5.1 x 10-7 kg; M = 80 kg

h = 19 cm = 0.19 m; v = 1.93 m/s

(A) KE = (1/2) m v2

      KE/m = (1/2) v2

(B) H/L = h/l

      H = (L/l)h

KE = PE

(1/2) M V2 = M g H

V = (2 g H)

(C) H = 60 (cm?) = 0.6 m

KE = PE

(1/2) M V2 = M g H

KE/M = g H

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