Question

Part AFind the x- and y-components of the vector d⃗ = (4.0 km , 29 ∘ left of +y-axis).Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.d⃗ = km Part BFind the x- and y-components of the vector v⃗ = (2.0 cm/s , −x-direction).Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.v⃗ = cm/s Part CFind the x- and y-components of the vector a⃗ = (13 m/s2 , 36 ∘ left of −y-axis).Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.a⃗ x = m/s2

Answer 1

Solution :

Part A .

Given : The $x$ and $y$ components of the vector, d = $\text{4 km 29}$ degree left of $y$-axis.

So the $x$ component is = -4 x sin (29°) = -1.939 km

           $y$ component is = 4 x cos (29°) = 3.498 km

Part B

Given : The $x$ and $y$ components of the vector, $\text{v = 2 cm/s}$ , $\text{-x direction}$

So the $x$ component is = -2 cm/s

           $y$ component is = 0

Part C

Given : The $x$ and $y$ components of the vector, $\text{a = 13 m/s, 36 degree}$ left of $y$-axis.

So the $x$ component is = -13 x sin (36°) = -7.6412 $m/S^2$

           $y$ component is = -13 x cos (36°) = -10.517 $m/S^2$

Answer 2

The x- and y-components of the vectors  is mathematically given as as follows for each Part respectively

x= -1.939 km, y= 3.498 km

x= -2 cm/s, 0

y=, x= -7.6412m/s^2, -10.517m/s^2

What are the x- and y-components of the vectors?

Question Parameters:

Generally, we follow a basic principle where

x component= Fsin\theta

y component= Fcos\theta

Therefore

For A

x component is

x= -4 x sin (29°)

x= -1.939 km

 y component is

y= 4 x cos (29°)

y= 3.498 km

For B

x component is

x= -2 cm/s            

y component is

y= 0

For C

x component is

x= -13 x sin (36°)

x= -7.6412m/s^2      

y component is

y= -13 x cos (36°)

y= -10.517m/s^2  

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