Question

The table represents the height of a rock that is dropped, h(t), in meters, after t seconds. (See picture.)

When does the rock hit the ground?

The rock hits the ground between ___ seconds and
___ seconds after it is dropped.

Answer 1

Answer: Between 2 and 2.5 seconds

How am I getting those values? Those values are selected from the 't' column on the left side of the table. These are time values in seconds. Note how t = 2 corresponds to h = 0.4; while t = 2.5 corresponds to h = -10.6

The change in sign for the height, from positive to negative, means that the height h must be zero at some point between t = 2 seconds and t = 2.5 seconds. We don't know where exactly, but we know that h = 0 at least once in this interval. This is because the height is a continuous function. There are no jumps or gaps in the height (the object can't teleport or anything)