### Problem DescriptionThe ice-hockey puck with a mass of 0.25 kg has a velocity of 10 m/s before being struck by the hockey stick. After the impact, the puck moves in the new direction shown with a velocity of 17 m/s. If the stick is in contact with the puck for 0.06 s, compute the magnitude of the average force \( F \) exerted by the stick on the puck during contact, and find the angle \( \beta \) made by \( F \) with the x-direction.---### Diagram ExplanationThe diagram depicts an ice-hockey puck and a hockey player. Here are the details of the diagram:- The initial velocity vector of the puck is shown as 10 m/s directed along the x-axis (to the left).- After being struck, the puck moves in a new direction at a velocity of 17 m/s, making an angle of 15 degrees with the x-axis.- The angles and directions are clearly marked with dashed lines, showing the path of the puck before and after impact.---### Solution#### Given Data:- Mass of the puck (\( m \)) = 0.25 kg- Initial velocity (\( v_i \)) = 10 m/s (along x-axis)- Final velocity (\( v_f \)) = 17 m/s (at 15° with x-axis)- Time of contact (\( t \)) = 0.06 s#### Required:- Magnitude of the average force (\( F \))- Angle (\( \beta \)) with the x-direction1. **Calculate the initial momentum (\( p_i \)) and final momentum (\( p_f \)) components:** Initial momentum: - \( p_{ix} = m \cdot v_i = 0.25 \cdot 10 = 2.5 \ \text{kg m/s} \) - \( p_{iy} = 0 \ \text{kg m/s} \) (since initial movement only along x-axis) Final momentum: - \( p_{fx} = m \cdot v_f \cdot \cos(15^\circ) \) - \( p_{fy} = m \cdot v_f \cdot \sin(15^\circ) \) Using \( \cos(15^\circ) \approx 0.965

To find: The magnitude and direction of the force. Given: The mass is m=0.25 kg. The final velocity…

The ice-hockey puck with a mass of 0.25 kg has a velocity of 10 m/s before being struck by the hockey stick. After the impact the puck moves in the new direction shown with a velocity of 17 m/s. If the stick is in contact with the puck for 0.06 s, compute the magnitude of the average force F exerted by the stick on the puck during contact, and find the angle 3 made by F with the x-direction. 10 m/s 15% 17 m/s ------

The ice-hockey puck with a mass of 0.25 kg has a velocity of 10 m/s before being struck by the hockey stick. After the impact the puck moves in the new direction shown with a velocity of 17 m/s. If the stick is in contact with the puck for 0.06 s, compute the magnitude of the average force F exerted by the stick on the puck during contact, and find the angle 3 made by F with the x-direction. 10 m/s 15% 17 m/s ------

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Problem Description

The ice-hockey puck with a mass of 0.25 kg has a velocity of 10 m/s before being struck by the hockey stick. After the impact, the puck moves in the new direction shown with a velocity of 17 m/s. If the stick is in contact with the puck for 0.06 s, compute the magnitude of the average force \( F \) exerted by the stick on the puck during contact, and find the angle \( \beta \) made by \( F \) with the x-direction.

---

### Diagram Explanation

The diagram depicts an ice-hockey puck and a hockey player. Here are the details of the diagram:

- The initial velocity vector of the puck is shown as 10 m/s directed along the x-axis (to the left).
- After being struck, the puck moves in a new direction at a velocity of 17 m/s, making an angle of 15 degrees with the x-axis.
- The angles and directions are clearly marked with dashed lines, showing the path of the puck before and after impact.

---

### Solution

#### Given Data:
- Mass of the puck (\( m \)) = 0.25 kg
- Initial velocity (\( v_i \)) = 10 m/s (along x-axis)
- Final velocity (\( v_f \)) = 17 m/s (at 15° with x-axis)
- Time of contact (\( t \)) = 0.06 s

#### Required:
- Magnitude of the average force (\( F \))
- Angle (\( \beta \)) with the x-direction

1. **Calculate the initial momentum (\( p_i \)) and final momentum (\( p_f \)) components:**

Initial momentum:
- \( p_{ix} = m \cdot v_i = 0.25 \cdot 10 = 2.5 \ \text{kg m/s} \)
- \( p_{iy} = 0 \ \text{kg m/s} \) (since initial movement only along x-axis)

Final momentum:
- \( p_{fx} = m \cdot v_f \cdot \cos(15^\circ) \)
- \( p_{fy} = m \cdot v_f \cdot \sin(15^\circ) \)

Using \( \cos(15^\circ) \approx 0.965

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