\(\displaystyle{h}={50}{\sin{{\left({6.0}\right)}}}={5.23}{m}\)

\(\displaystyle{m}{g}{h}=\frac{{1}}{{2}}{m}{v}^{{{2}}}\)

v = 10.1m/s

\(\displaystyle{m}_{{{c}}}\cdot{v}_{{{i}}}={m}_{{{f}}}\cdot{v}_{{{f}}}\)

\(\displaystyle{v}_{{{f}}}={m}_{{{c}}}\cdot\frac{{v}_{{{i}}}}{{m}_{{{f}}}}\)

\(\displaystyle{v}_{{{f}}}={6.97}\frac{{m}}{{s}}\cdot{5}{s}={34.8}\) (they have enough time).

b) \(\displaystyle\frac{{1}}{{2}}{m}_{{{i}}}\cdot{{v}_{{{i}}}^{{{2}}}}=\frac{{1}}{{2}}\cdot{m}_{{{f}}}\cdot{{v}_{{{f}}}^{{{2}}}}\)

\(\displaystyle\frac{{1}}{{2}}{\left({m}_{{{i}}}\cdot{{v}_{{{i}}}^{{{2}}}}-{m}_{{{f}}}\cdot{{v}_{{{f}}}^{{{2}}}}\right)}={4740}{J}\)

The kinetic energy decreased, this is to be expected with anon-elastic collision.

\(\displaystyle{m}{g}{h}=\frac{{1}}{{2}}{m}{v}^{{{2}}}\)

v = 10.1m/s

\(\displaystyle{m}_{{{c}}}\cdot{v}_{{{i}}}={m}_{{{f}}}\cdot{v}_{{{f}}}\)

\(\displaystyle{v}_{{{f}}}={m}_{{{c}}}\cdot\frac{{v}_{{{i}}}}{{m}_{{{f}}}}\)

\(\displaystyle{v}_{{{f}}}={6.97}\frac{{m}}{{s}}\cdot{5}{s}={34.8}\) (they have enough time).

b) \(\displaystyle\frac{{1}}{{2}}{m}_{{{i}}}\cdot{{v}_{{{i}}}^{{{2}}}}=\frac{{1}}{{2}}\cdot{m}_{{{f}}}\cdot{{v}_{{{f}}}^{{{2}}}}\)

\(\displaystyle\frac{{1}}{{2}}{\left({m}_{{{i}}}\cdot{{v}_{{{i}}}^{{{2}}}}-{m}_{{{f}}}\cdot{{v}_{{{f}}}^{{{2}}}}\right)}={4740}{J}\)

The kinetic energy decreased, this is to be expected with anon-elastic collision.