A baseball is hit from a height of 4.8 feet above the ground with an initial velocity of 136 feet per second and at an angle of 360 degrees above the horizontal.
What is the maximum height reached by the baseball? Neglect air resistance.

To solve for the maximum height reached by the baseball, we need to break down the motion into its vertical and horizontal components. Since air resistance is neglected, we only focus on the vertical component for calculating the maximum height.

Given dataTo solve for the maximum height reached by the baseball, we need to break down the motion into its vertical and horizontal components. Since air resistance is neglected, we only focus on the vertical component for calculating the maximum height.

Given 

- Initial height of the baseball: \( h_0 = 4.8 \text{ feet} \)
- Initial velocity: \( v_0 = 136 \text{ feet per second} \)
- Launch angle: \( \theta = 36^\circ \) (not 360 degrees, as 360° would be a horizontal shot, which is likely a typo or misunderstanding)
- Gravitational acceleration: \( g = 32.2 \text{ feet per second squared} \)

### Step 1: Vertical Component of Initial Velocity

The vertical component of the initial velocity is given by:

\[
v_{0y} = v_0 \sin(\theta)
\]

Substituting the values:

\[
v_{0y} = 136 \sin(36^\circ)
\]

We can calculate this component to proceed.

### Step 2: Maximum Height

The maximum height is reached when the vertical velocity becomes zero. Using the kinematic equation for vertical motion:

\[
v_{y}^2 = v_{0y}^2 - 2g(h_{\text{max}} - h_0)
\]

At the maximum height, \( v_y = 0 \), so:

\[
0 = v_{0y}^2 - 2g(h_{\text{max}} - h_0)
\]

Solving for \( h_{\text{max}} \):

\[
h_{\text{max}} = h_0 + \frac{v_{0y}^2}{2g}
\]

Let’s compute the values step by step.The maximum height reached by the baseball is approximately **104.03 feet**.

Would you like more details or have any questions? Here are five related questions to further explore this topic:

1. How long does it take for the baseball to reach its maximum height?
2. What is the total time the baseball stays in the air?
3. What is the horizontal distance traveled by the baseball before it hits the ground?
4. How would the result change if the angle of launch was increased to 45 degrees?
5. How does neglecting air resistance affect the trajectory of the baseball?

**Tip:** To maximize the range of a projectile (in the absence of air resistance), the optimal launch angle is 45 degrees.

A baseball is hit from a height of 4.8 feet above the ground with an initial velocity of 136 feet per second and at an angle of 360 degrees above the horizontal. What is the maximum height reached by the baseball? Neglect air resistance.

Learn how to calculate the maximum height reached by a baseball hit from 4.8 feet above the ground at a velocity of 136 feet per second and a 36-degree angle. Explore key concepts in projectile motion, kinematic equations, and trigonometry, perfect for high school students.

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