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Chapter 3: Q10P (page 57)

Find the (a) $x$ , (b) $y$ , and (c) $z$ components of the sum of the displacements and whose components in meters are $c_{x} = 7.4, c_{y} = 鈥� 3.8, c_{z} = 鈥� 6.1; d_{x} = 4.4, d_{y} = 鈥� 2.0, d_{z} = 3.3$

Short Answer

Expert verified

a) x component of is $c + d is 12 m$

b) y component of is $c + d is 鈥� 5.8 m$

c) z component of is $c + d is 鈥� 2.8 m$

Step by step solution

01

To calculate x component in meters

c and d are the displacement vectors. The sum of these vectors gives a resultant. Here the components of the resultant are to be found.

Given are the x, y z, components of the displacements c and d respectively.

$c_{x} = 7.4, c_{y} = - 3.8, c_{z} = - 6.1, d_{x} = 4.4, d_{y} = - 2.0, d_{y} = 3.3,$

The resultant of sum of displacements is given by

$R = c + d R_{x} = c_{x} + d_{x} (i) R_{y} = c_{y} + d_{y} (ii) R_{z} = c_{z} + d_{z} (iii)$

Substituting the above components in equation (i), the x component of R can be written as

$R_{x} = 7.4 + 4.4 R_{x} = 12 m$

02

To calculate y component in meters

$R_{y} = - 3.8 - 2.0 R_{y} = - 5.8 m$

03

To calculate z component in meters

$R_{z} = - 6.1 + 3.3 R_{z} = - 2.8 m$

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Most popular questions from this chapter

If is $\overset{鈬赌}{B}$ added to $\overset{鈬赌}{C} = 3.0 i + 4.0 \hat{j}$ , the result is a vector in the positive

direction of the y axis, with a magnitude equal to that of $\overset{鈬赌}{C}$ . What is the

magnitude of $\overset{鈬赌}{B}$ ?

Two vectors $\overset{鈫�}{a}$ and $\overset{鈫�}{b}$ have the components, in meters $a_{x} = 3.2$ ,role="math" localid="1657003775216" $a_{y} = 1.6$ , $b_{x} = 0.50$ , $b_{y} = 4.5$ ,(a) Find the angle between the directions of $\overset{鈫�}{a}$ and $\overset{鈫�}{b}$ .There are two vectors in the xy plane that are perpendicular to $\overset{鈫�}{a}$ and have a magnitude of 5.0 m. One, vector $\overset{鈫�}{c}$ , has a positive x component and the other, vector $\overset{鈫�}{d}$ , a negative x component. What are (b) the x component and (c) the y component of vector, and (d) the x component and (e) the y component of vector $\overset{鈫�}{d}$ ?

Vector $\overset{鈬赌}{A}$ which is directed along an x axis, which to be added to

vector $\overset{鈬赌}{B}$ , which has a magnitude of 7.0 m.The sum is a third vector that

is directed along the y axis, with a magnitude that is 3.0 times that of $\overset{鈬赌}{A}$ . What is that magnitude of $\overset{鈬赌}{A}$ ?

Let $\hat{i}$ be directed to the east, $\hat{j}$ be directed to the north, and be directed upward.What are the values of products (a) $\hat{i} . \hat{k}, (b) (- \hat{k}) . (\hat{j})$ , and (c) $(\hat{j}) . (- \hat{j})$ ? What are the directions (such as east or down) of products (d) $\hat{k} 脳 \hat{j}, (e) (- \hat{i}) 脳 (- \hat{j}), and (f) (- \hat{k}) 脳 (- \hat{j})$ ?

A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: $\overset{鈫�}{d_{1}}$ for 0.40 msouthwest (that is, at $45 掳$ from directly south and from directly west), $\overset{鈫�}{d_{2}}$ for 0.50 mdue east, $\overset{鈫�}{d_{3}}$ for 0.60 mat $60 掳$ north of east. Let the positive x direction be east and the positive y direction be north. What are (a) the x component and (b) the y component of $\overset{鈫�}{d_{1}}$ ? Next, what are (c) the x component and (d) the y component of $\overset{鈫�}{d_{2}}$ ? Also, what are (e) the x component and (f) the y component of $\overset{鈫�}{d_{3}}$ ?

What are (g) the x component, (h) the y component, (i) the magnitude, and (j) the direction of the ant鈥檚 net displacement? If the ant is to return directly to the starting point, (k) how far and (l) in what direction should it move?

See all solutions

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