Question

A particular cat flea (Ctenocephalides felis) has a mass of 5.0 x 10kg. Like most fleas, this one can jump many times higher than its own height. When jumping, it accelerates from rest through a distance of 0.40 mm, which allows it to reach a launch speed of 1.2 m/s, directed straight up. Use g = 9.8 m/s. [2 points] (a) Assuming constant acceleration, calculate the magnitude of the flea's acceleration while it is accelerating upward. [2 points] (b) For how much time does the flea have this acceleration? [2 points) (c) Sketch a free-body diagram of the flca, which applies while it is accelerating upward. [2 points) (d) What is the maximum height reached by the flea?

Answer 1

a) U=0, P-1. 2m 520.40mm From v2 = 1² + zas a> v²_u2 2 1.22-0 2 x 0.4 x 10-3 na = 1800 m/32 b) from v=utat -tv-u. " = 1.2-o 180 = 6:667x10-4 s. TF att flea F-mg = ma ,F force it requires to accelerate ufwand ma d? For beight reached after acceleration shops, h' u = 1.2 m/s height v =0 as 9 - - 9.8 m/s2 s=hl from y2 =42+2a5 ► 02 - 122 - 2x9.8 xh' h = 1.22 = 0.073469 m 2x9.8 = 74.469 mm total height reached H=h'ts = 74.469 mm + 0.40 um H = 0 73.8694 mm