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zepelin [54]
3 years ago
13

Two vectors A and B have components (0,1) and (-1,3) respectivly. What is the magnitude of the sum of these two vectors

Physics
1 answer:
Ymorist [56]3 years ago
3 0
A = <0,1>
B = <-1,3>
then
A + B = < 0+-1 , 1+3 > = <-1, 4>
magnitude = sqrt( (-1)^2 + (4)^2 )
= sqrt( 1 + 16)
= sqrt(17)
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Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different direc
Lapatulllka [165]

Answer:

a)     d = 30.79 m , b) θ = -22.4° ,   θ = 22.4 South of East

Explanation:

The easiest way to solve problems with vectors is to use their components, for this the East-West direction coincides with the x-axis and the North-South direction coincides with the y-axis

Let's use the index for / Ricardo and the index for Jane, let's break down the displacements

Richard

X axis

      x₁ = 26.0 sin (60)

      x₁ = -22.52 m

Y Axis  

     y₁ = 26.0 cos 60

     y₁ = 13 m / s

Jane

X axis

       x₂ = 16.0 cos (180 +30)

       x₂ = -13.85 m

Y Axis  

        y₂ = 16.0 sin (180 + 30)

        y₂ = - 8.0 m

Now we can use Pythagoras' theorem to find the distance between them

         d = √ [(x₂ -x₁)² + (y₂ -y₁)²]

         d = √ [(-13.85 + 22.52)² + (-8 -13)²]

         d = 30.79 m

Let's use trigonometry to enter the address

         tan θ = Δy / Δx

         θ = tan⁻¹ Δy / Δx

         θ = tan⁻¹ (-13.85 + 22.52) / (-8 - 13)

         θ = tan⁻¹ (-8.67 / 21)

         θ = -22.4°

The negative sign indicates that the angle is measured from the axis clockwise.

In the form of cardinal s point is

     θ = 22.4 South of East

4 0
4 years ago
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