Fleas have remarkable jumping ability. A 0.50 mg flea, jumping straight up, would reach a height of 40 cm if there were no air resistance. In reality, air resistance limits the height to 20 cm. a. What is the flea's kinetic energy as it leaves the ground?
b. At its highest point, what fraction of the initial kinetic energy has been converted to potential energy?

a. 1.96 X 10^-6  J

b. 1/2 Kinetic energy

Explanation:

The question above should be treated as an isolated system since it doesn't specify that energy is received or lost.

I/2m(vf)^2 + mg(xf) - I/2m(vi)^2 - mg(xi) = 0

Where: (vf) is final velocity, m is mass, (vi) is initial velocity, g is the acceleration due to gravity, (xf) is final distance, (xi) is the initial distance

I/2m(vf)^2 = 0, since (vf) = 0

mg(xi) = 0, since (xi) is the flea's distance at ground level

Therefore, mg(xf) - I/2m(vi)^2 = 0

mg(xf) = I/2m(vi)^2

The initial kinetic energy which is I/2m(vi)^2 = mg(xf)

0.5 X 10^-6 Kg X 9.8m/s2 X 0.4m = 1.96 X 10^-6  J

b.

The gravitational potential energy at its highest point

= 0.5 X 10^-6 Kg X 9.8m/s2 X 0.2m = 9.8 X 10^-7 J

Divide (9.8 X 10^-7 J by 1.96 X 10^-6  J)

we have = 1/2 Kinetic energy

one "light year" is the distance that light travels, through vacuum, in one julian year.   that's 365.25 days, of 24 hours each.