Given data
*The given mass is m = 800 kg
*The given height is h = 50 m
*The speed at point A is v_A = 20 m/s
*The height at point B is h_b = 12 m
(a)
The formula for the mechanical energy is given as
[tex]ME=U_k+U_p[/tex]
*Here U_k = 0 J is the kinetic energy
*Here U_p = mgh is the potential energy
Substitute the known values in the above expression as
[tex]\begin{gathered} ME=0+mgh \\ =800\times9.8\times50 \\ =392000\text{ J} \end{gathered}[/tex]
Hence, the mechanical energy is ME = 392000 J
(b)
The formula for the height at point A is given by the relation as
[tex]\begin{gathered} ME=U_K+U_P \\ U_p=ME-U_k \end{gathered}[/tex]
Substitute the known values in the above expression as
[tex]\begin{gathered} mgh_a=ME-\frac{1}{2}mv^2_A \\ 800\times9.8\times h_a=392000-\frac{1}{2}\times800\times(20)^2 \\ 7840h_a=232000 \\ h_a=29.5\text{ m} \\ \approx30\text{ m} \end{gathered}[/tex]
Hence, the height at point A is h_a = 30 m
(c)
The velocity at point B is calculated by the relation as
[tex]\begin{gathered} ME=U_K+U_P \\ U_K=ME-U_P \end{gathered}[/tex]
Substitute the known values in the above expression as
[tex]\begin{gathered} \frac{1}{2}mv^2_b=ME-mgh_b \\ \frac{1}{2}(800)(v^2_b)=392000-(800)(9.8)(12) \\ v_b=27.29\text{ m/s} \end{gathered}[/tex]
