### Problem StatementThe figure shows an overhead view of a 0.029 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. - Force \( \vec{F}_1 \) has a magnitude of 8 N and is at \( \theta_1 = 27^\circ \).- Force \( \vec{F}_2 \) has a magnitude of 10 N and is at \( \theta_2 = 30^\circ \).In unit-vector notation, what is the third force if the lemon half:(a) is stationary,(b) has the constant velocity \( \vec{v} = (12\hat{i} - 12\hat{j}) \) m/s,(c) has the velocity \( \vec{v} = (14t\hat{i} - 15t\hat{j}) \) m/s², where t is time?### Diagram DescriptionThe diagram features a yellow circle representing the lemon half at the origin of an x-y coordinate system with two forces acting on it. - The first force \( \vec{F}_1 \) is represented by a vector pointing upwards and slightly to the left, forming an angle \( \theta_1 \) of 27 degrees with the positive x-axis.- The second force \( \vec{F}_2 \) is represented by a vector pointing downwards and to the right, forming an angle \( \theta_2 \) of 30 degrees with the positive x-axis.### Input Fields for Solutions**(a)** Force \( \vec{F}_3 \) if the lemon half is stationary:- \( \text{Number} \) i + \( \text{Number} \) j \( \text{Units} \)**(b)** Force \( \vec{F}_3 \) if the lemon half has constant velocity \( \vec{v} = (12\hat{i} - 12\hat{j}) \) m/s:- \( \text{Number} \) i + \( \text{Number} \) j \( \text{Units} \)**(c)** Force \( \vec{F}_3 \) if the lemon half has a velocity \( \vec{v} = (14t\hat{i} - 15t\hat{j}) \) m/s

Answered: Image /qna-images/answer/4a4f6afe-cbe2-448e-9999-fbc6f5a210c1.jpg

The figure shows an overhead view of a 0.029 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force ₁ has a magnitude of 8 N and is at 0₁ = 27°. Force F2 has a magnitude of 10 N and is at 02 = 30°. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity = (12î - 123) m/s, and (c) has the v = (14tî - 15tĵ) m/s², where t is time? 0₁7 162 x

The figure shows an overhead view of a 0.029 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force ₁ has a magnitude of 8 N and is at 0₁ = 27°. Force F2 has a magnitude of 10 N and is at 02 = 30°. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity = (12î - 123) m/s, and (c) has the v = (14tî - 15tĵ) m/s², where t is time? 0₁7 162 x

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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Question

### Problem Statement

The figure shows an overhead view of a 0.029 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table.

- Force \( \vec{F}_1 \) has a magnitude of 8 N and is at \( \theta_1 = 27^\circ \).
- Force \( \vec{F}_2 \) has a magnitude of 10 N and is at \( \theta_2 = 30^\circ \).

In unit-vector notation, what is the third force if the lemon half:

(a) is stationary,

(b) has the constant velocity \( \vec{v} = (12\hat{i} - 12\hat{j}) \) m/s,

(c) has the velocity \( \vec{v} = (14t\hat{i} - 15t\hat{j}) \) m/s², where t is time?

### Diagram Description

The diagram features a yellow circle representing the lemon half at the origin of an x-y coordinate system with two forces acting on it.

- The first force \( \vec{F}_1 \) is represented by a vector pointing upwards and slightly to the left, forming an angle \( \theta_1 \) of 27 degrees with the positive x-axis.
- The second force \( \vec{F}_2 \) is represented by a vector pointing downwards and to the right, forming an angle \( \theta_2 \) of 30 degrees with the positive x-axis.

### Input Fields for Solutions

**(a)** Force \( \vec{F}_3 \) if the lemon half is stationary:
- \( \text{Number} \) i + \( \text{Number} \) j \( \text{Units} \)

**(b)** Force \( \vec{F}_3 \) if the lemon half has constant velocity \( \vec{v} = (12\hat{i} - 12\hat{j}) \) m/s:
- \( \text{Number} \) i + \( \text{Number} \) j \( \text{Units} \)

**(c)** Force \( \vec{F}_3 \) if the lemon half has a velocity \( \vec{v} = (14t\hat{i} - 15t\hat{j}) \) m/s

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