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3 years ago

For the two vectors A = (−5, 8) and B = (0, −6), find the components of A + B

Physics

1 answer:

harkovskaia [24]3 years ago

3 0

Answer:

(-5, 2)

Explanation:

We must remember that the components of a given point in a two-dimensional space are the points on an x & y coordinate axis

A = (-5, 8) = (x, y)

B = (0, -6) = (x, y)

Since the vector operation is a sum, we simply have to sum the components of x and the components of y.

A + B = (-5 + 0) , (8 + (-6))

A + B = (-5, 2)

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Calculate the Schwarzschild radius (in kilometers) for each of the following.1.) A 1 ×108MSun black hole in the center of a quas

Westkost [7]

Answer:

(I). The Schwarzschild radius is $2.94\times10^{8}\ km$

(II). The Schwarzschild radius is 17.7 km.

(III). The Schwarzschild radius is $1.1\times10^{-7}\ km$

(IV). The Schwarzschild radius is $7.4\times10^{-29}\ km$

Explanation:

Given that,

Mass of black hole $m= 1\times10^{8} M_{sun}$

(I). We need to calculate the Schwarzschild radius

Using formula of radius

$R_{g}=\dfrac{2MG}{c^2}$

Where, G = gravitational constant

M = mass

c = speed of light

Put the value into the formula

$R_{g}=\dfrac{2\times6.67\times10^{-11}\times1\times10^{8}\times1.989\times10^{30}}{(3\times10^{8})^2}$

$R_{g}=2.94\times10^{8}\ km$

(II). Mass of block hole $m= 6 M_{sun}$

We need to calculate the Schwarzschild radius

Using formula of radius

$R_{g}=\dfrac{2MG}{c^2}$

Put the value into the formula

$R_{g}=\dfrac{2\times6.67\times10^{-11}\times6\times1.989\times10^{30}}{(3\times10^{8})^2}$

$R_{g}=17.7\ km$

(III). Mass of block hole m= mass of moon

We need to calculate the Schwarzschild radius

Using formula of radius

$R_{g}=\dfrac{2MG}{c^2}$

Put the value into the formula

$R_{g}=\dfrac{2\times6.67\times10^{-11}\times7.35\times10^{22}}{(3\times10^{8})^2}$

$R_{g}=1.1\times10^{-7}\ km$

(IV). Mass = 50 kg

We need to calculate the Schwarzschild radius

Using formula of radius

$R_{g}=\dfrac{2MG}{c^2}$

Put the value into the formula

$R_{g}=\dfrac{2\times6.67\times10^{-11}\times50}{(3\times10^{8})^2}$

$R_{g}=7.4\times10^{-29}\ km$

Hence, (I). The Schwarzschild radius is $2.94\times10^{8}\ km$

(II). The Schwarzschild radius is 17.7 km.

(III). The Schwarzschild radius is $1.1\times10^{-7}\ km$

(IV). The Schwarzschild radius is $7.4\times10^{-29}\ km$

8 0

3 years ago

Which of the following statements is correct?

Mumz [18]

Answer: c. Generally, metals are ductile.

Explanation:

From the options given in the question, the correct statement is that"Generally, metals are ductile.

Ductility of a metal simply means that a metal can be plastically deform before it is then fractured. It implies that metals can be drawn to thin wires. The only exception we have in this case is mercury.

7 0

3 years ago

A typical jet airliner has a cruise airspeed of 900 km/h , which is its speed relative to the air through which it is flying. If

Luba_88 [7]

Explanation:

It is given that,

Speed of the jet airplane with respect to air, $v_{PA} = 900\ km/h$

If the wind at the airliner’s cruise altitude is blowing at 100 km/h from west to east, $v_{AG}= 100\ km/h$

(A) Let $v_{PG}$ is the speed of the airliner relative to the ground if the airplane is flying from west to east,

$v_{PG}=900-100=800\ km/h$

(B) Let $v'_{PG}$ is the speed of the airliner relative to the ground if the airplane is flying from east to west,

$v'_{PG}=900+100=1000\ km/h$

Hence, this is the required solution.

8 0

3 years ago

NEED ANSWER ASAP!!! Angela has a bucket of mass 2 kg tied to a string. She places a drinking glass of mass 0.5 kg in the bucket.

Schach [20]

a. The free-body diagram for the glass when it is at the top of the circle is attached below.

b. The equation for the net force on the glass at the top of the circle in terms of w, Fn, m, v, and r is mg x g + N - mg x Vtop² /R =0

c. The glass will fall out of the bucket if the normal force between the glass and bucket equals zero. The speed with which she spin the bucket to prevent this from happening is 3.83 m/s.

d. The string will break if the tension on it is more than 100 N. The range of speeds can prevent the string from breaking is 3.83< Vtop<4.99 m/s

<h3>What is Net force?</h3>

When two or more forces are acting on the system of objects, then the to attain equilibrium, net force must be zero.

Given, Angela has a bucket of mass 2 kg tied to a string. She places a drinking glass of mass 0.5 kg in the bucket. She spins the bucket in a vertical circle of radius 1.5 m. She must swing the bucket to keep the glass from falling out.

a. The free body diagram of the bucket and glass is attached below.

b. Bucket will undergo centrifugal force

Fb = mVtop² /R

From the equilibrium of forces, we have

For bucket,

T +mb xg - N = mb x Vtop² /R..............(1)

For glass,

mg x g + N = mg x Vtop² /R..............(2)

Thus, this is the net force equation on the glass.

c. On adding both the equations. we have

T + (mb + mg) xg = (mb + mg) Vtop² /R

Substituting the values, T = 0 and from the question, we get

0 + (2+0.5) 9.81 = (2+0.5)(Vtop²/0.5)

Vtop = 3.83 m/s

Thus, the speed of spin to prevent glass from falling out is 3.83 m/s

d. The string will break if the tension on it is more than 100 N

100 + (2+0.5) 9.81 = (2+0.5)(Vtop²/0.5)

Vtop = 4.99 m/s

Thus, the range of velocity is 3.83< Vtop<4.99 m/s

Learn more about net force.

brainly.com/question/18031889

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8 0

2 years ago

Natalie lifts a 15-kg rock from the ground onto a 1.5 meter high wall. what is the amount of potential energy she has given the

Zina [86]

The amount of gravitational potential energy acquired by the rock is equal to:
$\Delta U = mg \Delta h$
where
m is the mass of the rock
g is the gravitational acceleration
$\Delta h$ is the increase in height of the rock

Substituting the data of the problem, we find
$\Delta U=(15 kg)(9.81 m/s^2)(1.5 m)=220.7 J$
So, Natalie gave 220.7 J of energy to the rock.

4 0

3 years ago