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

b. What horizontal distance did it travel?

To find the horizontal distance (also known as the range) that the tennis ball traveled, we can use the following steps and formulas:

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

### Steps to Calculate Horizontal Distance:

1. **Horizontal Component of Velocity:**
   \[
   v_{0x} = v_0 \cos \theta
   \]

2. **Vertical Component of Velocity:**
   \[
   v_{0y} = v_0 \sin \theta
   \]

3. **Time of Flight:**
   The time of flight for a projectile can be calculated using:
   \[
   t = \frac{2 v_{0y}}{g}
   \]

4. **Horizontal Distance (Range):**
   The horizontal distance \( R \) is given by:
   \[
   R = v_{0x} \times t
   \]

### Calculations:

1. **Horizontal Component of Velocity:**
   \[
   v_{0x} = 65 \cos 38^\circ
   \]

2. **Vertical Component of Velocity:**
   \[
   v_{0y} = 65 \sin 38^\circ
   \]

3. **Time of Flight:**
   \[
   t = \frac{2 \times 65 \sin 38^\circ}{9.81}
   \]

4. **Horizontal Distance:**
   \[
   R = v_{0x} \times t
   \]

Let's compute these values step by step.The horizontal distance the tennis ball traveled is approximately **417.89 meters**.

Would you like further details or have any other questions?

Here are 5 related questions to consider:
1. How would the horizontal distance change if the angle of projection were increased?
2. What would be the effect of increasing the initial speed on the horizontal distance?
3. How would the time of flight change if the angle were 45 degrees?
4. What is the maximum height the ball reached during its flight?
5. How does air resistance impact the horizontal distance in real-world scenarios?

**Tip:** Always remember that the angle of 45° typically provides the maximum range for a projectile launched on a flat surface without air resistance.

Learn how to calculate the horizontal distance traveled by a tennis ball launched at 65 m/s with a 38° angle of projection. Includes step-by-step calculations using projectile motion and trigonometry. Suitable for high school physics students.

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