Required information A ball is thrown from a point 1.00 m above the ground. The initial velocity is 20.8 m/s at an angle of 30.0° above the horizontal. Calculate the speed of the ball at the highest point in the trajectory. m/s

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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### Physics Problem: Projectile Motion

#### Required Information:

A ball is thrown from a point 1.00 m above the ground. The initial velocity is 20.8 m/s at an angle of 30.0° above the horizontal.

**Task:**  
Calculate the speed of the ball at the highest point in the trajectory.

**Answer Input:**  
[Input box] m/s

### Explanation:

When a projectile is thrown, its motion can be separated into horizontal and vertical components. At the highest point in its trajectory, the vertical component of the velocity is zero, but the horizontal component remains constant throughout the motion.

**Initial Conditions:**
- Initial velocity (v₀): 20.8 m/s
- Angle of projection (θ): 30.0°
- Initial height: 1.00 m

**Calculating Components of Initial Velocity:**
- Horizontal Component: \( v_{0x} = v₀ \cdot \cos(\theta) \)
- Vertical Component: \( v_{0y} = v₀ \cdot \sin(\theta) \)

**Speed at the Highest Point:**
- At the highest point, the vertical velocity component becomes 0.
- Thus, the speed of the ball at the highest point is equal to its horizontal component \( v_{0x} \).

Using the given values, you can calculate \( v_{0x} \) to find the speed at the highest point.
Transcribed Image Text:### Physics Problem: Projectile Motion #### Required Information: A ball is thrown from a point 1.00 m above the ground. The initial velocity is 20.8 m/s at an angle of 30.0° above the horizontal. **Task:** Calculate the speed of the ball at the highest point in the trajectory. **Answer Input:** [Input box] m/s ### Explanation: When a projectile is thrown, its motion can be separated into horizontal and vertical components. At the highest point in its trajectory, the vertical component of the velocity is zero, but the horizontal component remains constant throughout the motion. **Initial Conditions:** - Initial velocity (v₀): 20.8 m/s - Angle of projection (θ): 30.0° - Initial height: 1.00 m **Calculating Components of Initial Velocity:** - Horizontal Component: \( v_{0x} = v₀ \cdot \cos(\theta) \) - Vertical Component: \( v_{0y} = v₀ \cdot \sin(\theta) \) **Speed at the Highest Point:** - At the highest point, the vertical velocity component becomes 0. - Thus, the speed of the ball at the highest point is equal to its horizontal component \( v_{0x} \). Using the given values, you can calculate \( v_{0x} \) to find the speed at the highest point.
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