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Chapter 3: Q. 4 (page 77)

A velocity vector 40°below the positive x-axis has a y-component of -10 m/s. What is the value of its x-component?

Short Answer

Expert verified

The value of its x-component is 11.92 m/s

Step by step solution

01

Step 1. Given information

The given values are,

The angle is $θ = 40^{0}$

y- component of the velocity is $v_{y} = - 10 m / s$

02

Step 2. Calculate the value of velocity v

Let velocity vector is $\vec{v}$ .

y- component of the velocity is

$v_{y} = - v \sin θ$

Put the value of y- component of the velocity

$- 10 = - v \sin 40^{0}$

$v = \frac{10}{\sin 40^{0}}$

03

Step 3. Calculate the value of x- component

We know that,

x- component of the velocity is

$v_{x} = v \cos θ$

Put the value of v and $θ$

$v_{x} = \frac{10}{\sin 40^{o}} \times \cos 40^{o}$

$v_{x} = 11.92 m / s$

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Most popular questions from this chapter

For the three vectors shown in FIGURE EX3.20, $\vec{A} + \vec{B} + \vec{C} = 1 \hat{j} .$ What is vector $\vec{B} ?$

a. Write $\vec{B}$ in component form.

b. Write $\vec{B}$ as a magnitude and a direction.

Is it possible to add a scalar to a vector? If so, demonstrate. If not, explain why not.

Let $\vec{A} = 4 \hat{i} - 2 \hat{j}$ , $\vec{B} = - 3 \hat{i} + 5 \hat{j}$ and $\vec{D} = \vec{A} - \vec{B}$ .

a. Write vector $\vec{D}$ in component form.

b. Draw a coordinate system and on it show vectors $\vec{A}, \vec{B}$ , and $\vec{D}$ .

c. What are the magnitude and direction of vector $\vec{D}$ ?

How would you define the zero vector $\vec{0} ?$

1. I Trace the vectors in FIGURE EX3.1 onto your paper. Then find

(a) $\vec{A} + \vec{B}$ and (b) $\vec{A} - \vec{B}$

See all solutions

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