### Upward Initial Velocity

1). 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? | 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 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. Solution | 2). After 3. 00 s of free-fall, what is the velocity v of the stone? Solution 1).

A football game customarily begins with a coin toss to determine who kicks off. The referee tosses the coin up with an initial speed of 5. 00 m/s. In the absence of air resistance, how high does the coin go above its point of release? Reasoning The coin is given an upward initial velocity. But the acceleration due to gravity points downward. Since the velocity and acceleration point in opposite directions, the coin slows down as it moves upward. Eventually, the velocity of the coin becomes v=0 m/s at the highest point. | At the start of a football game, a referee tosses a coin upward with an initial velocity of v0=+5. 0 m/s. The velocity of the coin is momentarily zero when the coin reaches its maximum height. | Solution| 2). What is the total time the coin is in the air before returning to its release point? Reasoning During the time the coin travels upward, gravity causes its speed to decrease to zero. On the way down, however, gravity causes the coin to regain the lost speed. Thus, the time for the coin to go up is equal to the time for it to come down. In other words, the total travel time is twice the time for the upward motion. With these data, we can use Equation (v=v0+at) to find the upward travel time. Solution