Question

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.

Answer 1

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/s²

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