During a baseball game, a batter hits a high
pop-up.
If the ball remains in the air for 6.66 s, how
high above the point where it hits the bat
does it rise? Assume when it hits the ground
it hits at exactly the level of the bat. The
acceleration of gravity is 9.8 m/s
2
.
Answer in units of m.

To determine how high the baseball rises, we can use the following kinematic equation:

\[
h = \frac{1}{2} g t^2
\]

Where:
- \( h \) is the height the ball reaches,
- \( g \) is the acceleration due to gravity (9.8 m/s²),
- \( t \) is the time the ball takes to reach the maximum height.

Given that the total time in the air is 6.66 seconds, the time to reach the highest point is half of this time (because the time to go up equals the time to come down):

\[
t = \frac{6.66}{2} = 3.33 \, \text{seconds}
\]

Now we can plug this value into the kinematic equation:

\[
h = \frac{1}{2} g t^2 = \frac{1}{2} (9.8) (3.33)^2
\]

Let's calculate this.The ball rises to a height of approximately 54.34 meters above the point where it was hit by the bat.

Would you like any more details on the calculation, or do you have any questions?

Here are 5 related questions you might find useful:
1. How does air resistance affect the time the ball stays in the air?
2. How would the height change if the acceleration due to gravity was different, such as on another planet?
3. What initial velocity did the ball have when it left the bat?
4. Can you calculate the total distance traveled by the ball, assuming it goes straight up and down?
5. How can we calculate the horizontal distance if the ball was hit at an angle?

**Tip:** When solving physics problems, always start by identifying what is given and what is being asked, then choose the appropriate equation.

During a baseball game, a batter hits a high pop-up. If the ball remains in the air for 6.66 s, how high above the point where it hits the bat does it rise? Assume when it hits the ground it hits at exactly the level of the bat. The acceleration of gravity is 9.8 m/s². Answer in units of m.

Learn how to calculate the maximum height reached by a baseball pop-up using kinematic equations. This problem involves understanding the concepts of projectile motion and free fall, applying the formula h = (1/2) * g * t^2, and is suitable for students in Grades 9-12.

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