Example 10 A Falling Stone

A stone is dropped from rest from the top of a tall building, as Figure 2.17 indicates. After 3.00 s of free-fall, what is the displacement y of the stone?

Figure 2.17 The stone, starting with zero velocity at the top of the building, is accelerated downward by gravity.

Reasoning The upward direction is chosen as the positive direction. The three known variables are shown in the box below. The initial velocity v₀ of the stone is zero, because the stone is dropped from rest. The acceleration due to gravity is negative, since it points downward in the negative direction.

Stone Data
y	a	v	v₀	t
?	–9.80 m/s²		0 m/s	3.00 s

Equation 2.8 contains the appropriate variables and offers a direct solution to the problem. Since the stone moves downward, and upward is the positive direction, we expect the displacement y to have a negative value.

Solution Using Equation 2.8, we find that

The answer for y is negative, as expected.