Vector C has a magnitude of 24.6 m and points in the − y ‑ direction. Vectors A and B both have positive y ‑ components, and make angles of α = 44.9 ° and β = 27.7 ° with the positive and negative x - axis, respectively. If the vector sum A + B + C = 0 , what are the magnitudes of A and B ?

A= 61.35

B= -44.40

Explanation:

1. Using the components method we have:

Considering that the vector sum , then:

Then:

It means the value of x and y component is 0.

2. Determinate the equations that describe each component:

Form Eq. (1):

Replacing A in Eq. (2):

Replacing values of C, α and β in (4):

Replacing value of B in (3)

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.