Oh Romeo, Romeo, wherefore art thou Romeo? In one of the lesser-known drafts of Romeo and...

 

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Oh Romeo, Romeo, wherefore art thou Romeo? In one of the lesser-known drafts of Romeo and Juliet, Romeo, Benvolio, and Mercutio are students at the Verona Institute of Technology. In this version of the famous balcony scene [ACT II, scene 2], Romeo vaults (in a sprightly manner) over the railing with the aid of a trebuchet that he and his friends had built as a class project. Our task, in aid of the star-cross'd lovers, is to calculate the launch parameters within the context of the model presented below. ♡ The balcony railing is 8m above ground and along the wall's edge. The tre- buchet arm releases its projectile at an initial height of 2m. There are no obstacles, and the ground is level adjacent to the structure. Take the acceleration due to gravity g = 10m/s². The effects of friction and drag are negligible. Romeo is moving horizontally, with speed 1m/s, as he clears the railing.¹ (a) Determine the launch speed and the initial angle that satisfy the design constraints, and how far, horizontally, away from the wall Romeo's launch point should be. (b) Romeo is accelerated from rest to his launch speed by the trebuchet arm. Let's say that the distance through which he moves while accelerating is 2m (the height at which he is released). Estimate the average acceleration that Romeo must endure to be launched. at the speed computed in (a). XCO Oh Romeo, Romeo, wherefore art thou Romeo? In one of the lesser-known drafts of Romeo and Juliet, Romeo, Benvolio, and Mercutio are students at the Verona Institute of Technology. In this version of the famous balcony scene [ACT II, scene 2], Romeo vaults (in a sprightly manner) over the railing with the aid of a trebuchet that he and his friends had built as a class project. Our task, in aid of the star-cross'd lovers, is to calculate the launch parameters within the context of the model presented below. ♡ The balcony railing is 8m above ground and along the wall's edge. The tre- buchet arm releases its projectile at an initial height of 2m. There are no obstacles, and the ground is level adjacent to the structure. Take the acceleration due to gravity g = 10m/s². The effects of friction and drag are negligible. Romeo is moving horizontally, with speed 1m/s, as he clears the railing.¹ (a) Determine the launch speed and the initial angle that satisfy the design constraints, and how far, horizontally, away from the wall Romeo's launch point should be. (b) Romeo is accelerated from rest to his launch speed by the trebuchet arm. Let's say that the distance through which he moves while accelerating is 2m (the height at which he is released). Estimate the average acceleration that Romeo must endure to be launched. at the speed computed in (a). XCO

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Part a To determine the launch speed and initial angle that satisfy the design constraints we can use the following equations of motion for a projecti... View the full answer