Answer
a) The flea's speed is $1.59m/s$
b) The flea moves $6.32\times10^{-4}m$ upward while it is pushing off.
Work Step by Step
(a) According to work-energy theorem, $KE_f=KE_0+W(1)$
The flea springs from rest so its initial speed $v_0=0$. This means its initial kinetic energy $KE_0=0$
The work done by the ground $W=2.4\times10^{-4}J$
So from (1), we get $KE_f=2.4\times10^{-4}J$
We know that $$KE_f=\frac{1}{2}mv_f^2=2.4\times10^{-4}J$$ $$v^2_f=\frac{4.8\times10^{-4}J}{m_{flea}}=\frac{4.8\times10^{-4}J}{1.9\times10^{-4}kg}=2.526m^2/s^2$$ $$v_f=1.59m/s$$
(b) The distance upward the flea moves is the magnitude of displacement, $s$.
We know $W=2.4\times10^{-4}J$ and $F=0.38N$. Both the force and the displacement point upward, so $\theta=0$. Therefore, $$s=\frac{W}{F\cos0}=6.32\times10^{-4}m$$
