https://file.aiquickdraw.com/mathbot/file/1729782002895x9vy6ihw.jpg

Let's work through the problem in the second box.

You need to find the time it takes for the ball to reach its maximum height. The initial upward velocity (\( v_0 \)) is 7.5 m/s (from the first problem), and the acceleration \( a \) due to gravity is \( -9.8 \, \text{m/s}^2 \).

To solve this, we use the kinematic equation for velocity:

\[
v = v_0 + at
\]

At the maximum height, the velocity \( v = 0 \), so we substitute into the equation:

\[
0 = 7.5 + (-9.8)t
\]

Solving for \( t \):

\[
t = \frac{-7.5}{-9.8} = 0.77 \, \text{seconds}
\]

Therefore, the time to reach the maximum height is 0.77 seconds.

Let me know if you'd like further explanation on any of these steps!

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Here are 5 related questions for further practice:
1. What would happen to the maximum height if the initial velocity were doubled?
2. How long would it take the volleyball to fall back down after reaching its peak?
3. How can you calculate the total flight time of the volleyball, considering both ascent and descent?
4. How would air resistance affect the volleyball's time and maximum height?
5. What formula would you use to find the maximum height if only time is known?

**Tip:** In kinematic problems, it's crucial to assign correct positive and negative signs for velocity and acceleration based on the direction of motion.

How long will it take the ball in the previous problem to reach its maximum height?

Solve for the time it takes a volleyball hit with an initial velocity of 7.5 m/s to reach its maximum height. This problem involves kinematics, the effects of gravity, and the use of the velocity-time formula. Suitable for students in Grades 9-11.

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