a
(a) Velocity by which the ball hits the bat

\({v_1} = \sqrt {2g{h_1}} = \sqrt {2 \times 10 \times 5} \) or \(\overrightarrow {{v_1}} = + 10\,m/s = 10\,m/s\)

velocity of rebound

\({v_2} = \sqrt {2g{h_2}} = \sqrt {2 \times 10 \times 20} = 20\,m/s\) or \(\overrightarrow {{v_2}} = - 20\,m/s\)

\(F = m\frac{{dv}}{{dt}} = \frac{{m(\overrightarrow {{v_2}} - \overrightarrow {{v_1}} )}}{{dt}} = \frac{{0.4( - 20 - 10)}}{{dt}} = 100\,N\)

by solving \(dt = 0.12\,\sec \)