# 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 .

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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

96% (84 ratings) ###### 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 .

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Our tutors have indicated that to solve this problem you will need to apply the Intro to Conservation of Energy concept. You can view video lessons to learn Intro to Conservation of Energy. Or if you need more Intro to Conservation of Energy practice, you can also practice Intro to Conservation of Energy practice problems.