It has been claimed that an insect called the froghopper (Philaenus spumarius) i

Question

It has been claimed that an insect called the froghopper (Philaenus spumarius) is the best jumper in the animal kingdom. This insect can accelerate at 3900 m/s2 over a distance of 2.3 mm as it straightens its specially designed "jumping legs."

(a) Assuming a uniform acceleration, what is the velocity of the insect after it has accelerated through this short distance, and how long did it take to reach that velocity?
velocity.............. m/s
elapsed time......... m/s

b) How high would the insect jump if air resistance could be ignored? Note that the actual height obtained is about 0.7 m, so air resistance is important here.

Explanation / Answer

the acceleration of the insect a = 3900m/s2, the short distance s = 2.3mm = 0.0023m,

if the intial velocity vi = 0m/s, its final velocity vf = ?

a) from Vf2 = vi2 +2as

vf2 = 0+2*3900*0.0023 = 17.94

vf = 4.23m/s

b) let the time taken t = ?

from vf = vi +at

t = (vf-vi)/a = (4.23-0)/3900 = 0.00108sec = 1.08milli sec

c) the height it can fly h = vf2/2g = (4.23*4.23)/(2*9.8)

h = 0.913m = 91.3cm

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