### Determining Velocity and Acceleration for a Backhoe BucketFor a short time, the bucket of the backhoe traces the path of the cardioid given by the equation\[ r = 25 (1 - \cos(\theta)) \] feet. The boom is rotating with an angular velocity of \[ \dot{\theta} = 1.8 \text{ rad/s} \] and an angular acceleration of \[ \ddot{\theta} = 0.17 \text{ rad/s}^2 \] at the instant shown in the image. In the figure, the backhoe's boom traces this path with an angle \( \theta = 120^\circ \).#### Diagram ExplanationThe diagram features an image of a backhoe loader with its boom extended to trace a cardioid path in the air. The bucket is positioned such that the angle \( \theta \) between the boom and the ground is \( 120^\circ \). This configuration represents the angle at which the calculations of velocity and acceleration should be determined.### Part A#### Calculating the Magnitude of VelocityDetermine the magnitude of the velocity of the bucket when \( \theta = 120^\circ \).**Instructions:** Express your answer to three significant figures and include the appropriate units.\[ v = \](Note: No hints were provided for this part.)### Part B#### Calculating the Magnitude of AccelerationDetermine the magnitude of the acceleration of the bucket when \( \theta = 120^\circ \).**Instructions:** Express your answer to three significant figures and include the appropriate units.\[ a = \](Note: No hints were provided for this part.)This educational exercise helps to understand the motion dynamics of mechanical parts in engineering using trigonometric and calculus concepts in a practical application. The analysis of velocity and acceleration at a specific point (\( \theta = 120^\circ \)) provides insight into the kinematic behavior of the system.

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For a short time the bucket of the backhoe traces the path of the cardioid r= 25(1- cos 0) ft. The boom is rotating with an angular velocity of å = 1.8 rad/s and an angular acceleration of = 0.17 rad/s at the instant shown. e- 120 Part A Determine the magnitude of the velooity of the bucket when 0- 120. Express your answer to three significant figures and include the appropriate units. You did not open hints for this par. Part B Determine the magnitude of the acceleration of the bucket when = 120°. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part

For a short time the bucket of the backhoe traces the path of the cardioid r= 25(1- cos 0) ft. The boom is rotating with an angular velocity of å = 1.8 rad/s and an angular acceleration of = 0.17 rad/s at the instant shown. e- 120 Part A Determine the magnitude of the velooity of the bucket when 0- 120. Express your answer to three significant figures and include the appropriate units. You did not open hints for this par. Part B Determine the magnitude of the acceleration of the bucket when = 120°. Express your answer to three significant figures and include the appropriate units. You did not open hints for this part

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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