Chapter 3: Q. 8 (page 77)

Let $\vec{C} = (3.15 m, 15^{\circ} a b o v e t h e n e g a t i v e x - a x i s)$ and $\vec{D} = (25.6 m, 30^{\circ} t o t h e r i g h t o f t h e n e g a t i v e y - a x i s) .$ Find the $x$ - and $y$ -components of each vector.

Short Answer

Expert verified

$C_{x} = - 3.04 m a n d C_{y} = 0.84 m .$

$D_{x} = 6.62 m a n d D_{y} = - 24.7 m .$ cc

Step by step solution

Step 1. Given informationff

It is given that $\vec{C} = (3.15 m, 15^{\circ} a b o v e t h e n e g a t i v e x - a x i s)$ and $\vec{D} = (25.6 m, 30^{\circ} t o t h e r i g h t o f t h e n e g a t i v e y - a x i s) .$ We need to determine the $x$ and $y$ components of each vector.

Step 2. Calculation

$\vec{C} = {\vec{C}}_{x} + {\vec{C}}_{y} .$

localid="1649188793381" ${\vec{C}}_{x} = C \cos 15^{\circ} .$

$= (- 3.15) \times 0.966 .$

$= - 3.04 m .$

${\vec{C}}_{y} = C \sin 15^{\circ} .$

$= (3.15) \times 0.26 .$

$= 0.84 m .$

$\vec{D} = {\vec{D}}_{x} + {\vec{D}}_{y} .$

localid="1651829724481" ${\vec{D}}_{x} = D \sin 30^{\circ}$

localid="1651829785442" $= (25.6) \times \sin 30^{\circ}$

localid="1651829836541" $= 12.8 m .$

${\vec{D}}_{y} = D \cos 15^{\circ} .$

localid="1651829797670" $= (- 25.6) \times \cos 30^{\circ}$

localid="1651829818366" $= - 22.17 m .$

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Let $\vec{C} = (3.15 m, 15^{\circ} a b o v e t h e n e g a t i v e x - a x i s)$ and $\vec{D} = (25.6 m, 30^{\circ} t o t h e r i g h t o f t h e n e g a t i v e y - a x i s) .$ Find the $x$ - and $y$ -components of each vector.

Short Answer

Step by step solution

Step 1. Given informationff

Step 2. Calculation

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Let C→=3.15m,15∘abovethenegativex-axisand D→=25.6m,30∘totherightofthenegativey-axis. Find the x- and y-components of each vector.

Short Answer

Step by step solution

Step 1. Given informationff

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

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Let $\vec{C} = (3.15 m, 15^{\circ} a b o v e t h e n e g a t i v e x - a x i s)$ and $\vec{D} = (25.6 m, 30^{\circ} t o t h e r i g h t o f t h e n e g a t i v e y - a x i s) .$ Find the $x$ - and $y$ -components of each vector.