A girl throws a ball at an inclined wall from a height of 3 ft, hitting the wall at A with a horizontal velocity vọ of magnitude 25 ft/s. Knowing that the coefficient of restitution between the ball and the wall is 0.9 and neglecting friction, determine the distance d from the foot of the wall to the Point B where the ball will hit the ground after bouncing off the wall. Vo 3 ft 60° C

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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### Problem Statement:
A girl throws a ball at an inclined wall from a height of 3 ft, hitting the wall at point \( A \) with a horizontal velocity \( v_0 \) of magnitude 25 ft/s. Knowing that the coefficient of restitution between the ball and the wall is 0.9 and neglecting friction, determine the distance \( d \) from the foot of the wall to the point \( B \) where the ball will hit the ground after bouncing off the wall.

### Diagram Explanation:
- **Initial Conditions**: The girl is positioned on the ground at the base of the wall.
- **Wall Inclination**: The wall is inclined at an angle of 60° from the horizontal.
- **Height**: The point where the ball is thrown from is at a height of 3 ft.
- **Trajectory**: The ball’s trajectory is depicted as a parabolic dashed line starting from the girl’s position, hitting point \( A \) on the inclined wall, then bouncing off and landing at point \( B \).
- **Velocity Vector**: An arrow labeled \( v_0 \) points horizontally from the girl’s position towards point \( A \), indicating the initial horizontal velocity of the ball.
- **Distance \( d \)**: This is the horizontal distance from the foot of the wall to point \( B \) where the ball hits the ground after bouncing off the wall.

This problem involves calculating the distance \( d \) by considering the properties of projectile motion and the coefficient of restitution to determine how the ball behaves after striking the inclined wall.
Transcribed Image Text:### Problem Statement: A girl throws a ball at an inclined wall from a height of 3 ft, hitting the wall at point \( A \) with a horizontal velocity \( v_0 \) of magnitude 25 ft/s. Knowing that the coefficient of restitution between the ball and the wall is 0.9 and neglecting friction, determine the distance \( d \) from the foot of the wall to the point \( B \) where the ball will hit the ground after bouncing off the wall. ### Diagram Explanation: - **Initial Conditions**: The girl is positioned on the ground at the base of the wall. - **Wall Inclination**: The wall is inclined at an angle of 60° from the horizontal. - **Height**: The point where the ball is thrown from is at a height of 3 ft. - **Trajectory**: The ball’s trajectory is depicted as a parabolic dashed line starting from the girl’s position, hitting point \( A \) on the inclined wall, then bouncing off and landing at point \( B \). - **Velocity Vector**: An arrow labeled \( v_0 \) points horizontally from the girl’s position towards point \( A \), indicating the initial horizontal velocity of the ball. - **Distance \( d \)**: This is the horizontal distance from the foot of the wall to point \( B \) where the ball hits the ground after bouncing off the wall. This problem involves calculating the distance \( d \) by considering the properties of projectile motion and the coefficient of restitution to determine how the ball behaves after striking the inclined wall.
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