Chapter 3: Q. 6 (page 77)

6. I Draw each of the following vectors. Then find its - and components.
a. $\vec{a} = (3.5 m / s^{2}$ , negative x-direction)
b. $\vec{v} = (440 m / s, 30^{°}$ below the positive x-axis )
c. $\vec{r} = (12 m, 40^{°}$ above the positive x-axis )

Short Answer

Expert verified

Part (a) x-component and y-component of the vectors are

$\begin{array}{l} x-component = 0 m / s^{2} \\ y-component = 3.5 m / s^{2} \end{array}$

Part (b) x-component and y-component of the vectors are

$\begin{array}{l} x-component = 381 m / s \\ y-component = - 220 m / s. \end{array}$

Part (c) x-component and y-component of the vectors are
$\begin{array}{l} x-component= 9.19 m \\ y-component = 7.71 m \end{array}$

Step by step solution

Given Information

a. $\vec{a} = (3.5 m / s^{2}$ , negative x -direction)

b. $\vec{v} = (440 m / s, 30^{°}$ below the positive x-axis )

c. $\vec{r} = (12 m, 40^{°}$ above the positive x-axis )

Parts (a)

Vector can be represented as below:

Here, $θ = 90^{°}$

x-component is

$\begin{array}{l} a_{x} = - a \cos θ \\ = - 3.5 m / s^{2} \times \cos 90^{°} \\ = - 3.5 m / s^{2} \times 0 \\ = 0 m / s^{2} \end{array}$

y-component is

$\begin{array}{l} a_{y} = a \sin θ . \\ = 3.5 m / s^{2} \times \sin 90^{°} \\ = 3.5 m / s^{2} \times 1 \\ = 3.5 m / s^{2} \end{array}$

$\begin{array}{l} x-component = 0 m / s^{2} \\ y-component = 3.5 m / s^{2} \end{array}$

Part (b)

Vector $\vec{v}$ can be represented as below:

x-component is

$\begin{array}{l} v_{x} = v \cos θ \\ = 440 m / s \times \cos 30^{°} \\ = 440 m / s \times 0.866 \\ = 381 m / s \end{array}$

y-component is

$\begin{array}{l} v_{y} = - v \sin θ \\ = - 440 m / s \times \sin 30^{°} \\ = - 440 m / s \times 0.5 \\ = - 220 m / s . \end{array}$

$\begin{array}{l} x-component = 381 m / s \\ y-component = - 220 m / s. \end{array}$

Part (c)

.c. Vector $\vec{r}$ can be represented as below:

x- component is

$\begin{array}{l} r_{x} = r \cos θ \\ = 12 m \times \cos 40^{°} \\ = 12 m \times 0.766 \\ = 9.19 m \end{array}$

y-component is

$\begin{array}{l} r_{y} = r \sin θ \\ = 12 m \times \sin 40^{°} \\ = 12 m \times 0.643 \\ = 7.71 m . \\ x-component= 9.19 m \\ y-component = 7.71 m \end{array}$

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6. I Draw each of the following vectors. Then find its - and components.
a. $\vec{a} = (3.5 m / s^{2}$ , negative x-direction)
b. $\vec{v} = (440 m / s, 30^{°}$ below the positive x-axis )
c. $\vec{r} = (12 m, 40^{°}$ above the positive x-axis )

Short Answer

Step by step solution

Given Information

Parts (a)

Part (b)

Part (c)

One App. One Place for Learning.

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6. I Draw each of the following vectors. Then find its - and components.a.a→=3.5m/s2, negative x-direction)b.v→=440m/s,30°below the positive x-axis )c.r→=12m,40° above the positive x-axis )

Short Answer

Step by step solution

Given Information

Parts (a)

Part (b)

Part (c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Physical Quantities And Units

Nuclear Physics

Turning Points in Physics

Radiation

Magnetism

Study anywhere. Anytime. Across all devices.

6. I Draw each of the following vectors. Then find its - and components.
a. $\vec{a} = (3.5 m / s^{2}$ , negative x-direction)
b. $\vec{v} = (440 m / s, 30^{°}$ below the positive x-axis )
c. $\vec{r} = (12 m, 40^{°}$ above the positive x-axis )