Must two quantities have the same dimensions if you are multiplying them?

Vector A with arrow, which is directed along an x axis, is to be added to vector B with arrow, which has a magnitude of 5.5 m. T

ohaa [14]

Answer:

Magnitude of vector A = 0.904

Explanation:

Vector A , which is directed along an x axis, that is

$\vec{A}=x_A\hat{i}$

Vector B , which has a magnitude of 5.5 m

$\vec{B}=x_B\hat{i}+y_B\hat{j}$

$\sqrt{x_{B}^{2}+y_{B}^{2}}=5.5\\\\x_{B}^{2}+y_{B}^{2}=30.25$

The sum is a third vector that is directed along the y axis, with a magnitude that is 6.0 times that of vector A $\vec{A}+\vec{B}=6x_A\hat{j}\\\\x_A\hat{i}+x_B\hat{i}+y_B\hat{j}=6x_A\hat{j}$

Comparing we will get

$x_A=-x_B\\\\y_B=6x_A$

Substituting in $x_{B}^{2}+y_{B}^{2}=30.25$

$\left (-x_{A} \right )^{2}+\left (6x_{A} \right )^{2}=30.25\\\\37x_{A}^2=30.25\\\\x_{A}=0.904$

So we have

$\vec{A}=0.904\hat{i}$

Magnitude of vector A = 0.904

8 0

3 years ago

Suppose a ball had a potential energy of 5 J when you dropped it.What would be it’s kinetic energy just as it hit the ground?

timama [110]

Answer:

Due to Conservation of Energy just as the ball hits the ground it's potential energy is assumed zero

Therefore disregarding air resistance all energy is converted into potential energy.

So KE = PE

(5 J)

4 0

3 years ago

Select all that apply. which of the following astronomers supported the sun-centered system? tycho brahe johannes kepler coperni

Alex73 [517]

<h3 />

-Tycho Brahe and

-Ptolemy

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The sun is a hot ball of glowing gases which is a star whose gravity holds the solar system together and also keeping all the planet and smallest particles of debris in its orbit.

3 0

3 years ago

Read 2 more answers

02: Describes what happens to the strength of gravity if the mass between two objects

Dmitriy789 [7]

Explanation:

The strength of the gravitational force between two objects depends on two factors, mass and distance. the force of gravity the masses exert on each other. ... increases, the force of gravity decreases. If the distance is doubled, the force of gravity is one-fourth as strong as before.

5 0

2 years ago

Find equation tangent to a circle at given point

vlabodo [156]

the equation of the tangent line must be passed on a point A (a,b) and perpendicular to the radius of the circle. <span>
I will take an example for a clear explanation:
let x² + y² = 4 is the equation of the circle, its center is C(0,0). And we assume that the tangent line passes to the point A(2.3).

</span>since the tangent passes to the A(2,3), the line must be perpendicular to the radius of the circle.

<span>Let's find the equation of the line parallel to the radius.</span>

<span>The line passes to the A(2,3) and C (0,0). y= ax+b is the standard form of the equation. AC(-2, -3) is a vector parallel to CM(x, y).</span>

det(AC, CM)= -2y +3x =0, is the equation of the line // to the radius.

let's find the equation of the line perpendicular to this previous line.

let M a point which lies on the line. so MA.AC=0 (scalar product),

it is (2-x, 3-y) . (-2, -3)= -4+4x + -9+3y=4x +3y -13=0 is the equation of tangent

7 0

3 years ago