Answer
a) $E_{lost}=2.82J$
b) $F=35.25N$
Work Step by Step
a) The energy lost can be found by looking at the differences in the height of the ball. In detail, $$E_{lost}=E_0-E_f=mg(h_0-h_f)$$
We know $m=0.6kg, h_f=0.57m, h_0=1.05m,$ and $ g=9.8m/s^2$
$$E_{lost}=2.82J$$
b) We call the dribbling force $F$. Since $F$ carries out work to make up for the loss of energy, we have $$W_F=E_{lost}=2.82J$$ $$(F\cos\theta)s=2.82J$$
$F$ is a downward force, so it points in the same direction as the ball; therefore, $\cos\theta=\cos0=1$. Also, $s=0.08m$
$$F=\frac{2.82}{0.08}=35.25N$$
