Given that

The mass of the stuntman is \(\displaystyle{\left({m}_{{{s}}}\right)}={80.0}{k}{g}\)

The mass of the movies villian is \(\displaystyle{\left({m}_{{{v}}}\right)}={70.0}{k}{g}\)

The distance between the window and floor is(y) =5.0m

The initial velocity is(u) =0

a)

By using the equation of motion we get that

The stuntman's speed before collision is \(\displaystyle{\left({v}_{{{0}}}\right)}=\sqrt{{{2}{g}{y}}}\)

The speed after collision is given by the conservation law

\(\displaystyle{v}={\left(\frac{{m}_{{{s}}}}{{m}_{{{s}}}}+{m}_{{{v}}}\right)}\cdot{v}_{{{0}}}\)

b)

The coefficient of kinetic friction of their bodies with thefloor is \(\displaystyle{\left(\mu_{{{k}}}\right)}={0.250}\)

During sliding momentum is not conserved.So, from the work-energy theorem we get that

Here x is the distance moved

\(\displaystyle\frac{{1}}{{2}}{m}_{{{t}}}{v}^{{{2}}}=\mu_{{{k}}}{m}_{{{t}}}{g}{h}\)

\(\displaystyle{x}=\frac{{v}^{{{2}}}}{{2}}\mu_{{{k}}}{g}\)

Now substitute all the values you get the required answer

The mass of the stuntman is \(\displaystyle{\left({m}_{{{s}}}\right)}={80.0}{k}{g}\)

The mass of the movies villian is \(\displaystyle{\left({m}_{{{v}}}\right)}={70.0}{k}{g}\)

The distance between the window and floor is(y) =5.0m

The initial velocity is(u) =0

a)

By using the equation of motion we get that

The stuntman's speed before collision is \(\displaystyle{\left({v}_{{{0}}}\right)}=\sqrt{{{2}{g}{y}}}\)

The speed after collision is given by the conservation law

\(\displaystyle{v}={\left(\frac{{m}_{{{s}}}}{{m}_{{{s}}}}+{m}_{{{v}}}\right)}\cdot{v}_{{{0}}}\)

b)

The coefficient of kinetic friction of their bodies with thefloor is \(\displaystyle{\left(\mu_{{{k}}}\right)}={0.250}\)

During sliding momentum is not conserved.So, from the work-energy theorem we get that

Here x is the distance moved

\(\displaystyle\frac{{1}}{{2}}{m}_{{{t}}}{v}^{{{2}}}=\mu_{{{k}}}{m}_{{{t}}}{g}{h}\)

\(\displaystyle{x}=\frac{{v}^{{{2}}}}{{2}}\mu_{{{k}}}{g}\)

Now substitute all the values you get the required answer