Answer
The change in the mechanical energy is $~~-12~J$
Work Step by Step
We can find the initial mechanical energy:
$E_0 = K_0+U_0$
$E_0 = \frac{1}{2}mv^2+0$
$E_0 = \frac{1}{2}(0.63~kg)(14~m/s)^2$
$E_0 = 61.74~J$
We can find the mechanical energy at maximum height:
$E_f = K_f+U_f$
$E_f = 0+mgh$
$E_f = (0.63~kg)(9.8~m/s^2)(8.1~m)$
$E_f = 50.01~J$
We can find the change in the mechanical energy:
$\Delta E = E_f - E_0$
$\Delta E = 50.01~J-61.74~J$
$\Delta E = -12~J$
The change in the mechanical energy is $~~-12~J$
