The height $h(t)$ at the time $t$ of a rock tossed into the air at time $0$ from an initial height $h_0$ at an initial velocity $v_0$ is given by $$h(t) = h_0 + v_0t - 16 t^2.$$ where time is measured in seconds, height in feet, and velocity in feet per second. The positive direction is up, so if the rock is moving down then its velocity is negative. The magic number 16 in this equation is due to the mass and radius of earth and would be different for example on Mars or on the Moon. The velocity of the rock at time $t$ is given by $$v(t) = v_0 -32t.$$ Suppose you throw a rock upward from a height of 64 feet with an initial velocity of 48 feet per second. The rock will hit the ground after seconds.

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