Law of conservation of energy:

$\overline{)\begin{array}{rcl}\mathbf{K}\mathbf{.}{\mathbf{E}}_{\mathbf{0}}\mathbf{+}\mathbf{P}\mathbf{.}{\mathbf{E}}_{\mathbf{0}}& {\mathbf{=}}& \mathbf{K}\mathbf{.}{\mathbf{E}}_{\mathbf{f}}\mathbf{+}\mathbf{P}\mathbf{.}{\mathbf{E}}_{\mathbf{f}}\\ \frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{+}{\mathbf{mgh}}_{\mathbf{0}}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}_{\mathbf{f}}}^{\mathbf{2}}\mathbf{+}{\mathbf{mgh}}_{\mathbf{f}}\end{array}}$

(a) At what height h above the ground does a projectile have a speed of 0.5v_{0}?

(b) What is the speed u of the object at the height of (1/2)h_{max}?

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