Physics, 04.09.2019 22:20 dxpebetty64

Two vectors, r and c, are equal: r = c. which of the following statements are true? (select all that apply.)
(a) the y-component of r must be equal to the y-component of c
(b) the x-component of r must be equal to the x-component of c
(c) the z-component of r must be equal to the z-component of c
(d) the directions of r and c may be different
(e) the magnitudes of r and c may be different
(f) the unit vector r must be equal to the unit vector c.

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Answer from: oliviahopebigel

(A) The y-component of r must be equal to the y-component of c

(B) The x-component of r must be equal to the x-component of c

(F) The unit vector r must be equal to the unit vector c.

Explanation:

If two vectors are equal there are some conditions must be satisfy for the two vectors to be equal.

Let us suppose 2 vectors as,

$A=a_{1}i+ a_{2}j+a_{3}k$ and

$B=b_{1}i+ b_{2}j+b_{3}k$

The conditions for the above two vectors should be equal are:

(1) $a_{1}=b_{1}$ , $a_{2}=b_{2}$ , and $a_{3}=b_{3}$ .

(2) Unit vector of A must be equal to unit vector of B.

(3) Magnitude of both the vectors should be equal.

Now, according to question and observing above conditions of equality for r and c to be equal, the statements should be true are:

(A) The y-component of r should be equal to the y-component of c

(B) The x-component of r should be equal to the x-component of c

(F) The unit vector r should be equal to the unit vector c.

Answer from: Quest

here we know that ball will drop down by total distance 3.2 m

so here we know that

$v_{yi} = 0$

$\delta y = - 3.2 m$

now using kinematics

$\delta y = v_{yi} t + \frac{1}{2}at^2$

$-3.2 = 0 -\frac{1}{2}(9.8) t^2$

$t = 0.81 s$

now in the same time it will cover horizontal distance of 0.75 m

$\delta x = 0.75m$

so speed of the ball will be

$v = \frac{delta x }{\delta t}$

$v = \frac{0.75}{0.81} = 0.93 m/s$

Answer from: Quest

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.

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Two vectors, r and c, are equal: r = c. which of the following statements are true? (select all th...

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