Answer:
The flea will move high to a height of 0.05 meters.
Explanation:
Given that,
Acceleration of the flea, [tex]a=1000\ m/s^2[/tex]
Distance, d = 0.5 mm = 0.0005 m
Let u and v are the initial and final velocity of the flea. Using equation of motion as :
[tex]v^2-u^2=2ad[/tex]
[tex]v^2-u^2=2\times 1000\times 0.0005[/tex]
[tex]v^2-u^2=1[/tex]..........(1)
Using conservation of energy, we get :
[tex]\dfrac{1}{2}mu^2=\dfrac{1}{2}mv^2+mgh[/tex]
[tex]\dfrac{1}{2}u^2=\dfrac{1}{2}v^2+(-g)h[/tex]
[tex]\dfrac{1}{2}u^2=\dfrac{1}{2}v^2-gh[/tex]
[tex]\dfrac{1}{2g}(u^2-v^2)=-h[/tex]
[tex]h=\dfrac{1}{2g}[/tex]
[tex]h=\dfrac{1}{2\times 9.8}[/tex]
h = 0.05 meters
So, the flea will move high to a height of 0.05 meters. Hence, this is the required solution.
