A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in the figure below. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m. m/s 40.0° 2.00 3.05 m 10.0 m

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Chapter1: Units, Trigonometry. And Vectors
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**Projectile Motion in Basketball**

A 2.00-meter-tall basketball player is standing on the floor 10.0 meters from the basket, as illustrated in the diagram. The player shoots the ball at a 40.0° angle with the horizontal. The question asks: at what initial speed must the player throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 meters.

**Diagram Explanation:**

- **Initial Position**: The basketball player is indicated at the left part of the diagram, 2.00 meters tall.
- **Trajectory**: The basketball's path is shown as an arc starting from the player and moving towards the hoop.
- **Horizontal Distance**: The distance between the player and the hoop is marked as 10.0 meters.
- **Angle of Launch**: The launch angle of the ball is illustrated as 40.0° from the horizontal.
- **Basket Height**: The basketball hoop is shown to be 3.05 meters high.
- There's an arrow indicating the peak point in the trajectory and aiming towards the hoop.

This setup is typical for understanding projectile motion, considering elements like initial velocity, angle of projection, and gravitational force.
Transcribed Image Text:**Projectile Motion in Basketball** A 2.00-meter-tall basketball player is standing on the floor 10.0 meters from the basket, as illustrated in the diagram. The player shoots the ball at a 40.0° angle with the horizontal. The question asks: at what initial speed must the player throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 meters. **Diagram Explanation:** - **Initial Position**: The basketball player is indicated at the left part of the diagram, 2.00 meters tall. - **Trajectory**: The basketball's path is shown as an arc starting from the player and moving towards the hoop. - **Horizontal Distance**: The distance between the player and the hoop is marked as 10.0 meters. - **Angle of Launch**: The launch angle of the ball is illustrated as 40.0° from the horizontal. - **Basket Height**: The basketball hoop is shown to be 3.05 meters high. - There's an arrow indicating the peak point in the trajectory and aiming towards the hoop. This setup is typical for understanding projectile motion, considering elements like initial velocity, angle of projection, and gravitational force.
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