To calculate the maximum height reached by the ball, we can use the kinematic equation for vertical motion under constant acceleration due to gravity. When the ball reaches its maximum height, its final vertical velocity will be zero.

Given dataTo calculate the maximum height reached by the ball, we can use the kinematic equation for vertical motion under constant acceleration due to gravity. When the ball reaches its maximum height, its final vertical velocity will be zero.

Given

• Initial velocity ($v_0$) = 15.0 m/s
• Final velocity ($v$) = 0 m/s (at the maximum height)
• Acceleration due to gravity ($g$) = -9.8 m/s² (negative because gravity acts downward)

We use the following kinematic equation:

$v^2 = v_0^2 + 2 \cdot a \cdot h$

Where:

• $v$ is the final velocity,
• $v_0$ is the initial velocity,
• $a$ is the acceleration (gravity in this case),
• $h$ is the height.

Step-by-Step Solution:

1. Substitute the values into the equation:

   $0 = (15.0)^2 + 2 \cdot (-9.8) \cdot h$

2. Simplify the equation:

   $0 = 225 - 19.6 \cdot h$

3. Solve for $h$:

   $19.6 \cdot h = 225$

   $h = \frac{225}{19.6}$

   $h \approx 11.5 \text{ m}$

Answer:

The maximum height reached by the ball is approximately 11.5 meters.

Would you like a more detailed explanation, or do you have further questions?

Here are some related questions for further practice:

1. What is the time taken to reach the maximum height?
2. What will be the total time of flight of the ball?
3. If Mario throws the ball with a different initial velocity, how would the maximum height change?
4. How would the maximum height change if gravity were different?
5. What would be the velocity of the ball after 1 second?

Tip: When calculating vertical motion, remember that gravity's effect on acceleration is always negative (downward) in the equations if upward is taken as positive.