**Vectors and Resultants: Calculating the Y-Component****Given:**- \(\vec{a} = (0, -3)\)- \(\vec{b} = (2, 0)\)**Problem:**Find the y-component of the resultant vector:\[\vec{r} = 2 \vec{a} + 3 \vec{b}\]**Solution:**We start with the given vectors:\(\vec{a} = (0, -3)\)\(\vec{b} = (2, 0)\)We need to calculate the resultant vector:\[\vec{r} = 2 \vec{a} + 3 \vec{b}\]First, we scale each vector:\[2 \vec{a} = 2(0, -3) = (0, -6)\]\[3 \vec{b} = 3(2, 0) = (6, 0)\]Next, we add the scaled vectors to get the resultant vector \(\vec{r}\):\[\vec{r} = (0, -6) + (6, 0) = (6, -6)\]Finally, the y-component of the resultant vector \(\vec{r} = (6, -6)\) is:\[y \text{-component} = -6\]Thus, the y-component of the resultant vector is \(-6\).

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Given vectors a=(0,-3) and b=(2,0) Find the y-component of the resultant vector: T = 2a + 36

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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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

**Vectors and Resultants: Calculating the Y-Component**

**Given:**
- \(\vec{a} = (0, -3)\)
- \(\vec{b} = (2, 0)\)

**Problem:**
Find the y-component of the resultant vector:
\[\vec{r} = 2 \vec{a} + 3 \vec{b}\]

**Solution:**

We start with the given vectors:
\(\vec{a} = (0, -3)\)
\(\vec{b} = (2, 0)\)

We need to calculate the resultant vector:
\[\vec{r} = 2 \vec{a} + 3 \vec{b}\]

First, we scale each vector:
\[2 \vec{a} = 2(0, -3) = (0, -6)\]
\[3 \vec{b} = 3(2, 0) = (6, 0)\]

Next, we add the scaled vectors to get the resultant vector \(\vec{r}\):
\[\vec{r} = (0, -6) + (6, 0) = (6, -6)\]

Finally, the y-component of the resultant vector \(\vec{r} = (6, -6)\) is:
\[y \text{-component} = -6\]

Thus, the y-component of the resultant vector is \(-6\).

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