**Problem Context:**Romeo (75.0 kg) entertains Juliet (49.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from Juliet, who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on Romeo's cheek.**Questions:**(a) **How far (in m) does the 79.0 kg boat move toward the shore it is facing?**- Solution Box: ____ m(b) **What If?** If the lovers both walk toward each other and meet at the center of the boat, how far (in m) and in what direction does the boat now move?- Magnitude Box: ____ m- Direction Dropdown: [Select]

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Description: **Problem Context:**Romeo (75.0 kg) entertains Juliet (49.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from Juliet, who is in the front of the boat. After the serenade, Juliet carefully moves to the rea

Answered: Romeo (75.0 kg) entertains Juliet (49.0…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Problem Context:**

Romeo (75.0 kg) entertains Juliet (49.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from Juliet, who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on Romeo's cheek.

**Questions:**

(a) **How far (in m) does the 79.0 kg boat move toward the shore it is facing?**

- Solution Box: ____ m

(b) **What If?** If the lovers both walk toward each other and meet at the center of the boat, how far (in m) and in what direction does the boat now move?

- Magnitude Box: ____ m
- Direction Dropdown: [Select]

Expert Solution

Step 1: Distance moved by the boat

The center of mass of the boat, Romeo and Juliet system can be given as,

Here, m and x represent the mass and position, respectively.

Here, the subscripts J, R, and B represents Juliet, Romeo, and Boat, respectively.

Let Juliet’s position be the origin. The boat’s mass can be considered at the mid of the boat.

Thus, substituting the values we can write

$X_{c m, i} = \frac{((49 \times 0) + (75 \times 2.70) + (79 \times 1.35))}{49 + 75 + 79}$

$X_{c m, i} = 1.523 m$

now, when Juliet moves to the rear, the position of the center of mass can be given as,

substitute the relevant values.

$X_{c m, f} = \frac{((49 + 75) \times 2.70) + (79 \times 1.35))}{49 + 75 + 79}$

$X_{c m, f} = 2.174 m$

The system’s center of mass does not change with respect to the water because no external force acts on the system.

The change in the position of the center of mass is the distance that is moved by boat.

Thus, the distance moved by boat is,

Substitute the relevant values.

$d = X_{c m, f} - X_{c m, i}$

$\Rightarrow d = 2.174 - 1.523$

$=> d = 0.651 m$

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