# Problem: An object is thrown directly upward with some initial speed v.Using conservation of energy, find the maximum height hmax to which the object will rise.Express your answer in terms of v and the magnitude of the acceleration of gravity g .

###### FREE Expert Solution

Conservation of energy:

$\overline{)\begin{array}{rcl}\mathbf{P}{\mathbf{E}}_{\mathbf{i}}\mathbf{+}\mathbf{K}{\mathbf{E}}_{\mathbf{i}}& {\mathbf{=}}& \mathbf{P}{\mathbf{E}}_{\mathbf{f}}\mathbf{+}\mathbf{K}{\mathbf{E}}_{\mathbf{f}}\\ \mathbf{m}\mathbf{g}{\mathbf{h}}_{\mathbf{i}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{{\mathbf{v}}_{\mathbf{i}}}^{\mathbf{2}}& {\mathbf{=}}& \mathbf{m}\mathbf{g}{\mathbf{h}}_{\mathbf{f}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{{\mathbf{v}}_{\mathbf{f}}}^{\mathbf{2}}\end{array}}$

vi = v m/s,  vf = 0 m/s, hi = 0m, hf = hmax

###### Problem Details

An object is thrown directly upward with some initial speed v.

Using conservation of energy, find the maximum height hmax to which the object will rise.

Express your answer in terms of v and the magnitude of the acceleration of gravity g .