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a) Calculate the direction in degrees of the final velocity of the bowling ball, relative to its initial direction of travel. b) calculate the magnitude of the final velocity, in meters per second, of the bowling ball.

a) Calculate the direction in degrees of the final velocity of the bowling ball, relative to its initial direction of travel. b) calculate the magnitude of the final velocity, in meters per second, of the bowling ball.

Elements Of Electromagnetics
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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a) Calculate the direction in degrees of the final velocity of the bowling ball, relative to its initial direction of travel.

b) calculate the magnitude of the final velocity, in meters per second, of the bowling ball.

**Problem Description:** An \( m_1 = 5.25 \)-kg bowling ball moving at an initial velocity \( v_{i1} = 8.50 \) m/s collides with an \( m_2 = 0.725 \) kg bowling pin, which is scattered at an angle of \( \theta_2 = 20.5^\circ \) from the initial direction of the bowling ball, with a speed of \( v_{2f} = 10.1 \) m/s. **Diagrams and Explanation:** - The diagram is divided into two main sections: "Before" and "After" the collision. **Before the Collision:** - The bowling ball \( (m_1) \) is represented moving to the right with an initial velocity \( v_{i1} \). - The bowling pin \( (m_2) \) is shown at rest. **After the Collision:** - The bowling ball \( (m_1) \) has a final velocity \( v_{1f} \) in a direction different from the initial one. - The pin \( (m_2) \) is scattered at an angle \( \theta_2 = 20.5^\circ \) below the horizontal axis (initial direction of the bowling ball) with a velocity \( v_{2f} = 10.1 \) m/s. **Concepts Illustrated:** - Conservation of momentum in two dimensions. - Change of direction and velocity post-collision. - Angular displacement from the initial direction for \( m_2 \). This scenario is typical in physics to understand momentum and vector decomposition in collisions.
Transcribed Image Text:**Problem Description:** An \( m_1 = 5.25 \)-kg bowling ball moving at an initial velocity \( v_{i1} = 8.50 \) m/s collides with an \( m_2 = 0.725 \) kg bowling pin, which is scattered at an angle of \( \theta_2 = 20.5^\circ \) from the initial direction of the bowling ball, with a speed of \( v_{2f} = 10.1 \) m/s. **Diagrams and Explanation:** - The diagram is divided into two main sections: "Before" and "After" the collision. **Before the Collision:** - The bowling ball \( (m_1) \) is represented moving to the right with an initial velocity \( v_{i1} \). - The bowling pin \( (m_2) \) is shown at rest. **After the Collision:** - The bowling ball \( (m_1) \) has a final velocity \( v_{1f} \) in a direction different from the initial one. - The pin \( (m_2) \) is scattered at an angle \( \theta_2 = 20.5^\circ \) below the horizontal axis (initial direction of the bowling ball) with a velocity \( v_{2f} = 10.1 \) m/s. **Concepts Illustrated:** - Conservation of momentum in two dimensions. - Change of direction and velocity post-collision. - Angular displacement from the initial direction for \( m_2 \). This scenario is typical in physics to understand momentum and vector decomposition in collisions.
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