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Chapter 3: Q. 19 (page 78)

What are the $x$ - and $y$ -components of the velocity vector shown in FIGURE EX3.19?

Short Answer

Expert verified

$x$ - component $= 50 m / s .$

$y$ -component $= 86.6 m / s .$

Step by step solution

01

Step 1. Given information

The given figure is,

We need to determine the $x a n d y$ components of the velocity shown in the figure.

02

Step 2. Solution

It is given that $θ = 30 a n d v = 100 m / s .$

Thus $100 \times \sin 30^{\circ} .$

$= 50$ in the $x$ direction,

and $100 \times \cos 30^{\circ} .$

$= 86.6$ in the $y$ direction.

Hence, the $x$ -component $= 50 m / s .$

$y$ -component $= 86.6 m / s .$

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Most popular questions from this chapter

If $\vec{C} = \vec{A} + \vec{B},$ Can $C > A + B ?$ For each, show how or explain why not

II Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction.

a. $\vec{A} = 3 \hat{i} + 7 \hat{j}$

b. $a = (- 2 \hat{i} + 4.5 \hat{j}) m / s^{2}$

c. $\vec{v} = (14 \hat{i} - 11 \hat{j}) m / s$

d. $\vec{r} = (- 2.2 \hat{i} - 3.3 \hat{j}) m$

Let $\vec{A} = 4 \hat{i} - 2 \hat{j}, \vec{B} = - 3 \hat{i} + 5 \hat{j} a n d \vec{F} = \vec{A} - 4 \vec{B} .$

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

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

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

FIGURE $P 3.26$ shows vectors $\vec{A} & \vec{B}$ . Find $\vec{D} = 2 \vec{A} + \vec{B}$ . Write your answer in component form.

Dee is on a swing in the playground. The chains are 2.5 m long, and the tension in each chain is 450 N when Dee is 55 cm above the lowest point of her swing. Tension is a vector directed along the chain, measured in newtons, abbreviated N. What are the horizontal and vertical components of the tension at this point in the swing?

See all solutions

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