A vector A⃗ has a magnitude of 40.0 m and points in a direction 20.0 ∘ below the positive x axis. A second vector, B⃗ , has a magnitude of 75.0 m and points in a direction 50.0 ∘ above the positive x axis.

a) Sketch the vectors A⃗ , B⃗ , and C⃗=A⃗+B⃗ .

b) Using the component method of vector addition, find the magnitude of the vector C⃗ .

c) Using the component method of vector addition, find the direction of the vector C

The analytical method of the components allows to find the results for the questions about the sum vector are:

     a) In the attached we have a scheme of the vectors

     b) the modulus is C = 96.3 m

     c) The angle is θ = 27.0º

Given parameters

To find

    a) Draw the vectors and their sum.

    b) The module.

    c) the adirection.

The sum of vectors has several methods of resolution:

The analytical method consists:

In the attached we have a diagram of each vector and its sum. Let's use trigonometry to find the component of each vectors.

Vector A

            cos θ₁ =  

            sin θ₁ =  

            Aₓ = A cos θ₁

            = A sin θ₁

            Aₓ = 40 cos (-20) = 37.59 m

            = 40 sin (-20) = -13.68 m

Vector B

           cos θ₂ =  

           sin θ₂ =  

           Bₓ = B cos θ₂

            = B sin θ₂

           Bₓ = 75 cos 50 = 48.21 m

            = 75 sin 50 = 57.45 m

we add the components.

           Cₓ = Aₓ + Bₓ

           Cₓ = 37.59 + 48.20 = 85.8 m

           Cy = -13.68 + 57.45 = 43.8 m

b) We use the Pythagorean theorem to find the modulus of the resultant vector.

          C² = Cₓ² +  

          C =  

         C = 96.3 m.

c) We use trigonometry to find the angle of the resultant vector.

         tan θ =  

         θ = tan⁻¹  

         θ = tan⁻¹  

         θ = 27.0º

In conclusion, using the analytical method of the components we can find the results for the questions about the sum vector are:

     a) In the attached we have a scheme of the vectors

     b) the modulus is C = 96.3 m

     c) The angle is θ = 27.0º

Learn more about vector addition here:  link

Explanation:

Check attachment for solution

multiply 2kg by latent heat of vap