Answer:
Explanation:
The given equation is:
[tex]\frac{1}{2}mv^2+mgh=E[/tex]
Note that:
The mass m is constant
Total energy E is constant
The derivative of a constant is zero
g = 9.81 m/s^2
dh/dt = v
Compute d/dt of both sides
[tex]\begin{gathered} \frac{d}{dt}(\frac{1}{2}mv^2)+\frac{d}{dt}(mgh)=\frac{dE}{dt} \\ \\ \frac{1}{2}m\frac{d}{dt}(v^2)+mg\frac{dh}{dt}=0 \\ \\ \frac{1}{2}(m)(2v)\frac{dv}{dt}+mgv=0 \\ \\ mv\frac{dv}{dt}+mgv=0 \\ \\ mv\frac{dv}{dt}+9.81mv=0 \\ \\ mv(\frac{dv}{dt}+9.81)=0 \\ \\ \frac{dv}{dt}+9.81=0 \\ \\ \frac{dv}{dt}=-9.81\text{ m/s}^2 \end{gathered}[/tex]
