Consider two vectors, A = 16.5 m at 48.0°, and B = (-12.7 + 2.30j) m.Determine the x and y components of A:AxAym.Determine the x and y components of B:B.Let H- B- 3 A. Determine H and express it in unit vector form.1+コ)-HDetermine the magnitude and direction of HH=mat3:

The given vectors, A→=16.5 m at 48°B→=-12.7 i^+2.30 j^ m The x and y components of A vector,…

Answered: Consider two vectors, A = 16.5 m at…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 50P: Consider the three displacement vectors A=(3i3j)m, B=(i4j)m, and C=(2i+5j)m. Use the component...

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Question

Consider two vectors, A = 16.5 m at 48.0°, and B = (-12.7 + 2.30j) m.
Determine the x and y components of A:
Ax
Ay
m.
Determine the x and y components of B:
B.
Let H- B- 3 A. Determine H and express it in unit vector form.
1+
コ)-H
Determine the magnitude and direction of H
H=
mat
3:

Expert Solution

Step 1

The given vectors,

$\begin{array}{rcl} \vec{A} & = & 16.5 m at 48 ° \\ \vec{B} & = & (- 12.7 \hat{i} + 2.30 \hat{j}) m \end{array}$

The x and y components of A vector,

$\begin{array}{rcl} A_{x} & = & (16.5 m) \cos (48 °) \\ = & 11.04 m \\ A_{y} & = & (16.5 m) \sin (48 °) \\ = & 12.26 m \end{array}$

Step 2

So, the vector A in unit vector form

$\vec{A} = (11.04 \hat{i} + 12.26 \vec{j}) m$

The x and y components of B vector,

$\begin{array}{rcl} B_{x} & = & - 12.7 m \\ B_{y} & = & 2.30 m \end{array}$

Step 3

The H vector,

$\vec{H} = \vec{B} - 3 \vec{A}$

Substitute,

$\begin{array}{rcl} \vec{H} & = & (- 12.7 \hat{i} + 2.30 \vec{j}) m - 3 (11.04 \hat{i} + 12.26 \vec{j}) m \\ = & (- 45.82 \hat{i} - 34.48 \vec{j}) m \end{array}$

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