Solution

A projectile is launched vertically upward from an initial height of $s_0$ feet with an initial velocity of $v_0$ ft/s. Neglecting air resistance, show that its height $s(t)$ above the ground at time $t$ is given by $s(t) = -\dfrac{1}{2}gt^2 + v_0 t + s_0$ where $g > 0$ is the magnitude of the acceleration due to gravity.