A tennis ball is hit with an initial speed of 65m/s at a 380 angle with the horizontal.
c. How high did it go?

To determine the maximum height the tennis ball reaches, we need to analyze the vertical component of the ball's motion. Here’s how we can approach it:

### Step 1: Resolve the initial velocity into components
The initial velocity (\(v_0\)) is 65 m/s, and the angle (\(\theta\)) is 38°.

- The vertical component of the velocity (\(v_{0y}\)) is given by:
\[
v_{0y} = v_0 \sin(\theta)
\]

### Step 2: Apply the kinematic equation for vertical motion
At the maximum height, the vertical velocity becomes zero (\(v_y = 0\)). The kinematic equation that relates the initial velocity, final velocity, acceleration, and displacement is:
\[
v_y^2 = v_{0y}^2 - 2g h
\]
where:
- \(v_y\) is the final vertical velocity (0 m/s at maximum height),
- \(g\) is the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)),
- \(h\) is the maximum height.

Rearranging for \(h\), we get:
\[
h = \frac{v_{0y}^2}{2g}
\]

### Step 3: Calculate the values
First, find \(v_{0y}\):
\[
v_{0y} = 65 \times \sin(38^\circ)
\]

Now, plug this into the equation for \(h\).

Let me calculate that.The maximum height the tennis ball reaches is approximately **81.71 meters**.

Would you like more details or have any questions? Here are five related questions to consider:

1. What is the time it takes for the tennis ball to reach its maximum height?
2. What is the total time the tennis ball spends in the air?
3. How far horizontally does the tennis ball travel before hitting the ground?
4. How would the maximum height change if the ball were hit at a different angle?
5. What would happen to the maximum height if the initial speed were increased?

**Tip:** In projectile motion, the vertical and horizontal motions are independent of each other, and gravity only affects the vertical motion.

Learn how to calculate the maximum height reached by a tennis ball launched at 65 m/s with a 38° angle. This problem covers projectile motion and kinematics, involving formulas such as vertical velocity component and kinematic equations. Suitable for Grades 10-12 students.

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