A tennis ball is hit with an initial speed of 65m/s at a 380 angle with the horizontal.

a. How long was he ball in the air?

To determine how long the tennis ball was in the air, we need to analyze the vertical motion of the ball. The horizontal motion is not directly relevant to the time of flight.

Given:
- Initial speed, \( v_0 = 65 \, \text{m/s} \)
- Angle with the horizontal, \( \theta = 38^\circ \)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)

### Steps to solve:

1. **Calculate the vertical component of the initial velocity:**

   The vertical component of the initial velocity \( v_{0y} \) can be found using:
   \[
   v_{0y} = v_0 \sin \theta
   \]

   Substituting the given values:
   \[
   v_{0y} = 65 \times \sin 38^\circ
   \]

2. **Determine the time of flight:**

   The total time of flight \( T \) for a projectile is given by:
   \[
   T = \frac{2v_{0y}}{g}
   \]

Let's calculate this.

### 1. Calculate the vertical component of the initial velocity:
\[
v_{0y} = 65 \times \sin 38^\circ \approx 65 \times 0.6157 \approx 40.02 \, \text{m/s}
\]

### 2. Determine the time of flight:
\[
T = \frac{2 \times 40.02}{9.81} \approx \frac{80.04}{9.81} \approx 8.16 \, \text{seconds}
\]

### Final Answer:
The tennis ball was in the air for approximately **8.16 seconds**.

Would you like to go into more details or have any other questions?

Here are some related questions:

1. What would be the maximum height reached by the tennis ball?
2. What is the range of the tennis ball?
3. How would the time of flight change if the angle was 45°?
4. How does the time of flight change if the initial speed is increased?
5. What is the horizontal distance covered by the ball before it lands?

**Tip:** When solving projectile motion problems, it's helpful to break the motion into horizontal and vertical components, as they are independent of each other.

Learn how to calculate the time of flight for a tennis ball launched with an initial speed of 65m/s at a 38-degree angle. This problem involves analyzing projectile motion and trigonometric functions. Suitable for high school physics students.

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