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

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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.