Displacement vector A points due east and has a magnitude of 1.9 km. Displacement vector B points due north and has a magnitude of 2.08 km. Displacement vector C points due west and has a magnitude of 2.4 km. Displacement vector D points due south and has a magnitude of 2.8 km. Find the magnitude and direction (relative to due east) of the resultant vector A + B + C + D

Explanation:

We shall represent all the four displacement in vector form  in terms of unit vector i and j where i represents unit vector towards east , j represents unit vector towards north .

Displacement of A

D₁ = 1.9 i

Displacement of B

D₂ = 2.08 j

Displacement of C

D₃ = - 2.4 i

Displacement of D

D₄ = -2.8 j

Resultant displacement

= 1.9 i + 2.08 j - 2.4 i - 2.8 j

= - 0.5 i - 0.72 j

magnitude of resultant vector

= √ ( .5² + .72² )

=√ ( .25 + .5184 )

= √ .7684

= .876 km

Both i and j are negative of resultant displacement

hence its direction is towards south of west . Angle with west is Ф .

TanФ = .5184 / .25 = 2.0736

Ф = 64.25° .

From east direction is  = 180 + 64.25 = 244.25° .

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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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.