The mass of the child, m = 22 kg
Height, h = 2.5 m
The child starts at rest
The initial velocity, u = 0
Workdone on the child, W = -381 J
The child's speed at the bottom of the slide is the final speed
Final speed, v = ?
Based on the principle of energy conservation
Kinetic Energy = Potential energy + Non-conservative workdone
[tex]\frac{1}{2}mv^2=mgh+W[/tex]Substitute m = 22, g = 9.8, h = 2.5, and W = -381 into the equation above
[tex]\begin{gathered} \frac{1}{2}\times22\times v^2=(22\times9.8\times2.5)+(-381) \\ \\ 11v^2=539-381 \\ \\ 11v^2=158 \\ \\ v^2=\frac{158}{11} \\ \\ v^2=14.36 \\ \\ v=\sqrt{14.36} \\ \\ v=3.79\text{ m/s} \end{gathered}[/tex]