The final velocity of a rock tossed straight up and falling into a hole can be determined using kinematic equations. When the rock returns to its original launch height, its velocity equals the initial launch velocity but in the opposite direction. To calculate the final velocity as the rock hits the bottom of the hole, one must know the depth of the hole and apply the appropriate kinematic relation, such as \( v^2 = u^2 + 2as \), where \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is the acceleration due to gravity, and \( s \) is the depth of the hole.
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