(b) what is the initial y-component of the velocity? (use energy methods)

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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I only need anwer for b

**Physics Problem: Initial Velocity Component**

**Question**:
(b) What is the initial y-component of the velocity? (Use energy methods)

This question asks for the initial vertical component of the velocity in a given physical scenario, specifically requesting to find the solution by applying energy methods. This implies that you will need to use principles such as the conservation of energy, kinetic energy, potential energy, and related formulas to determine the initial velocity in the y-direction.
Transcribed Image Text:**Physics Problem: Initial Velocity Component** **Question**: (b) What is the initial y-component of the velocity? (Use energy methods) This question asks for the initial vertical component of the velocity in a given physical scenario, specifically requesting to find the solution by applying energy methods. This implies that you will need to use principles such as the conservation of energy, kinetic energy, potential energy, and related formulas to determine the initial velocity in the y-direction.
### Problem Statement:
A 0.04-kg ball is thrown from the top of a 30-m tall building (point A) at an unknown angle above the horizontal. As shown in the figure, the ball attains a maximum height of 10 m above the top of the building before striking the ground at point B. If air resistance is negligible,

(a) What is the y-component of the ball’s velocity at point B? (Use energy methods)

### Explanation of the Figure:
The figure illustrates a trajectory of the ball, which starts at point A on top of a 30-meter tall building. The ball is launched at an unknown angle above the horizontal. It reaches a maximum height of 10 meters above point A. After reaching this peak height, the ball descends and strikes the ground at point B.

- **Point A**: The launch point, located at the top of the 30-meter tall building.
- **Maximum Height**: The ball rises 10 meters above the top of the building before it starts descending.
- **Point B**: The point where the ball strikes the ground. The total vertical distance from point A to B is 30 meters.

### Energy Considerations:
To find the y-component of the ball's velocity at point B, we use energy methods:

- **Potential Energy at the Maximum Height**: Consider the maximum height reached by the ball (10 meters above the building top).
- **Kinetic Energy Just Before Impact**: At point B, just before hitting the ground, the potential energy would have converted into kinetic energy due to gravitational acceleration.

By applying the conservation of mechanical energy:
\[ \text{Total Mechanical Energy at point A} = \text{Total Mechanical Energy at point B} \]

Let \( m \) be the mass of the ball, \( g \) be the acceleration due to gravity, \( h_1 \) be the initial height (30 meters), and \( h_2 \) be the maximum height (10 meters above the building). The initial kinetic energy and potential energy can be expressed in terms of these known quantities.

By calculating the changes in potential energy and equating it to the kinetic energy at point B, we can isolate and solve for the y-component of the velocity at impact.

Overall, the energy method will give us the y-component of the velocity by focusing on the conversion between potential and kinetic energy as the ball moves from point A, through its maximum height,
Transcribed Image Text:### Problem Statement: A 0.04-kg ball is thrown from the top of a 30-m tall building (point A) at an unknown angle above the horizontal. As shown in the figure, the ball attains a maximum height of 10 m above the top of the building before striking the ground at point B. If air resistance is negligible, (a) What is the y-component of the ball’s velocity at point B? (Use energy methods) ### Explanation of the Figure: The figure illustrates a trajectory of the ball, which starts at point A on top of a 30-meter tall building. The ball is launched at an unknown angle above the horizontal. It reaches a maximum height of 10 meters above point A. After reaching this peak height, the ball descends and strikes the ground at point B. - **Point A**: The launch point, located at the top of the 30-meter tall building. - **Maximum Height**: The ball rises 10 meters above the top of the building before it starts descending. - **Point B**: The point where the ball strikes the ground. The total vertical distance from point A to B is 30 meters. ### Energy Considerations: To find the y-component of the ball's velocity at point B, we use energy methods: - **Potential Energy at the Maximum Height**: Consider the maximum height reached by the ball (10 meters above the building top). - **Kinetic Energy Just Before Impact**: At point B, just before hitting the ground, the potential energy would have converted into kinetic energy due to gravitational acceleration. By applying the conservation of mechanical energy: \[ \text{Total Mechanical Energy at point A} = \text{Total Mechanical Energy at point B} \] Let \( m \) be the mass of the ball, \( g \) be the acceleration due to gravity, \( h_1 \) be the initial height (30 meters), and \( h_2 \) be the maximum height (10 meters above the building). The initial kinetic energy and potential energy can be expressed in terms of these known quantities. By calculating the changes in potential energy and equating it to the kinetic energy at point B, we can isolate and solve for the y-component of the velocity at impact. Overall, the energy method will give us the y-component of the velocity by focusing on the conversion between potential and kinetic energy as the ball moves from point A, through its maximum height,
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