During a baseball game, a batter hits a high pop-up. If the ball remains in the air for 6.82 s, how high does it rise? The acceleration of gravity is 9.8 m/s².

The answer is 56.98 m

The dislocation (d) is:

d = v1 * t + 1/2 * a * t²

v1 - initial velocity

t - time

a - acceleration of gravity

We know:

d = ?

v1 = ?

t = 6.82 s / 2 = 3.41 (it reaches the peak at half time)

a = - 9.8 m/s ²

Let's first calculate v1:

v2 = v1 + at

v2 - final velocity (v2 = 0 when it reaches peak)

0 = v1 + - 9.8 * 3.41

0 = v1 - 33.418

v1 = 33.418 m/s

d = v1 * t + 1/2 * a * t²

d = 33.418 * 3.41 + 1/2 * - 9.8 * 3.41²

d = 113.96 - 56.98

d = 56.98 m