Example 6 The Time of Flight of a Kickoff

For the motion illustrated in Figure 3.12, ignore air resistance and use the data from Example 5 to determine the time of flight between kickoff and landing.

Reasoning Given the initial velocity, it is the acceleration due to gravity that determines how long the ball stays in the air. Thus, to find the time of flight we deal with the vertical part of the motion. Since the ball starts at and returns to ground level, the displacement in the y direction is zero. The initial velocity component in the y direction is the same as that in Example 5; that is, v_0y=+14 m/s. Therefore, we have

y-Direction Data
y	a_y	v_y	v_0y	t
0 m	–9.80 m/s²		+14 m/s	?

The time of flight can be determined from Equation 3.5b

Solution Using Equation 3.5b, we find

There are two solutions to this equation. One is given by

The other is given by

. The solution we seek is

, because

corresponds to the initial kickoff.