A rock is thrown upwards and has a max altitude of 40 m. What was its initial velocity?

Recall the formula,

where and are the rock's initial and final velocities, respectively; is its acceleration; and is the displacement it undergoes.

At any point during its motion, the rock is subject to gravity, so , where . At its maximum height, the rock has zero vertical velocity, and if we take its starting height to be the origin, we have .

So,

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