(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 $