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Anettt [7]
3 years ago
6

A vector A has components Ax = −4.00 m and Ay = 3.50 m. Find the magnitude (in m) and the direction (in degrees counterclockwise

from the +x-axis) of the vector.
Physics
1 answer:
8_murik_8 [283]3 years ago
4 0

Answer:

Part (i) the magnitude of the vector is 5.315 m

Part (ii) the direction of the vector is 138.8⁰

Explanation:

Given;

y-component Ay = 3.50 m

x -component Ax = -4.00 m

Vector representation = (-4i + 3.5j)

Part (i) the magnitude of the vector

Magnitude of the vector = √(-4)² +(3.5)²

Magnitude of the vector = √28.25

                                          = 5.315 m

Part (ii) the direction (in degrees counterclockwise from the +x-axis) of the vector.

If we make a rough sketch of this vector, the direction of this vector lies in second quadrant.

That is; 90 < θ < 180

Let's solve for θ

tan θ = y/x

tan θ = 3.5/-4

tan θ = - 0.875

θ = tan⁻¹ (-0.875)

θ = - 41.2⁰

Since θ lies in the second quadrant,

θ = - 41.2⁰ = 180 - 41.2 = 138.8⁰

The direction of the vector is 138.8⁰

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Determine the weight in newtons of a woman whose weight in pounds is 157. Also, find her mass in slugs and in kilograms. Determi
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Answer:

Weight of the woman in Newton

   x =  698.6 \  N

 Mass of the woman in slug

  Mass =  4.86 \  slug

 Mass of the woman in kg

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  My weight in Newton

  W =  784 \  N

Explanation:

From the question we are told that

   The weight of the woman in pounds is  W = 157 \ lb

Converting to Newton

    1 N  =  0.22472 lb

    x N  =  157

=>   x =  \frac{157 *  1}{0.22472}

=>   x =  698.6 \  N

Obtaining the mass in slug

   Mass =  \frac{W}{g}

Here  g =  32.2 ft/s^2

So

     Mass =  \frac{157 }{32.2}

       Mass =  4.86 \  slug

Obtaining the mass in kilogram

     Mass =  \frac{W}{g}

Here  g =  9.8 \  m/s

So

   Mass =  \frac{157 }{9.8}

   Mass =  16 \  kg

Generally weight is mathematically represented as

     W =  m *  g

Given that my mass is   80 kg   then my weight is  

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