What is the component of 3i^ + 4j^ along i^+j^

Answers

Answer 1

Answer:

The required component of vector is 7√2/2 unit.

What is unit vector?

Physical quantities that exhibit both magnitude and direction are referred to as vector quantities. As an illustration, consider displacement, force, torque, momentum, acceleration, and velocity.

Typically, an arrow is used on top of a vector quantity to depict the vector value of the velocity and to clarify that the quantity has both magnitude and direction.

A quantity with both magnitude and direction is referred to as a vector. A unit vector is one with a magnitude of 1. It also goes by the name Direction Vector.

Given vector is :

$\vec{A} =3\hat{i} + 4\hat{j}$ .

and the other vector is :

$\vec{B} = \hat{i} + \hat{j}$ .

The unit vector along $\vec{B}$ is

$\hat B =\frac{ \hat{i} + \hat{j}}{√(2) }$

Hence, component of A vector along B vector is =

$\vec{A}.\vec{B}$

= $(3\hat{i} + 4\hat{j}).\frac{ \hat{i} + \hat{j}}{√(2) }$

= (3+4)/√2

= 7/√2

= 7√2/2 unit.

So, the required component of vector is 7√2/2 unit.

Learn more about vector here:

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Answer 2

Answer: using the Pythagorean theorem

a^2 = b^2 + c^2

when a is the hypotenuse, and b and c are opposites and adjacent in a right triangle

3^2 + 4^2 = 5^2

Therefore, the hypotenuse has a magnitude of 5

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Select all of the following that describes momentum, p [mark all correct answers] a. momentum is the product of mass and acceleration
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Answers

Answer:

c. Momentum is the product of mass and velocity

e. Momentum is a vector quantity

g. Momentum has unit of kgm/s

Explanation:

Linear momentum P

P = m .v

m =mass

v=Velocity

If mass take in kg and velocity is in m/s then momentum p will be in kg.m/s.

1. momentum is the product of velocity and mass.

2.Momentum is a vector quantity.

3.Momentum have kg.m/s unit.

So the following option are correct.

c. Momentum is the product of mass and velocity

e. Momentum is a vector quantity

g. Momentum has unit of kgm/s.

Note-

1.Joule is the unit of energy.

2.One-half the product of mass and the square of the object's speed is known as kinetic energy.

The diagram below shows a 1.5 kilogram kitten jumping from the top of a 1.80 meter high refrigerator to a 0.90 meter highcounter.
Refrigerator
Counter
CO
The kitten's gravitational potential energy on top of the refrigerator is greater, but what is the kitten's gravitational
potential energy on top of the counter? Assume gravity as 10, if needed.

Answers

Answer:

E = 27 J

Explanation:

It is given that,

Mass of a kitten is 1.5 kg

Initially, it was at a height of 1.8 m refrigerator and finally jumps to a 0.9 m height counter.

We need to find the kitten's gravitational potential energy on top of the counter. Potential energy is possessed due to the position of an object. It can be given by :

$E=mgh$

g is acceleration due to gravity

$E=1.5\ kg* 10\ m/s^2* 1.8\ m\nE=27\ J$

So, the kitten's gravitational potential energy on top of the counter is 27 J.

The four terrestrial planets that have solid, rocky surfaces are A. Mars, Venus, Earth, and Jupiter.
B. Mercury, Jupiter, Saturn, and Mars.
C. Mercury, Venus, Jupiter, and Mars.
D. Mercury, Venus, Earth, and Mars

Answers

The four terrestrial planets that hace solid, rocky surfaces are (D.) Mercury, Venus, Earth, and Mars.

Check out pages 804-808 in the Glencoe Earth Science textbook provided by PennFoster. That way you can learn about the answer. :)

A particle with velocity v(t)=1/t−3, in m/s, moves in a straight line. Its initial displacement is known to be s(1)=1, in m. Find the position function s(t).

Answers

Answer:

s(t) = (t1 - t2)* [((1/t1 - 3) + (1/t0 - 3))/2]

Explanation:

We will assume that v(t) is in units of m/s and t (time) is in seconds.

v(t)=1/t−3

At time 0 (initial) the equation tells us the particle has a velocity of

v(t)=1/t−3

v(0)=1/(0)−3

v(0) = - 3 m/s

The particle is moving from right to left (the negative sign) at a rate of 3 m/s.

The position of the particle would be the average velocity times the time traveled.

Distance = Velocity x Time (with Velocity being the average between times t0 and t1)

We'll use s(t) for displacement for time t.

s(t) = v*t

We need the average velocity for the time period t0 to t1.

Let t0 and t1 be the initial and final times in which the measurement takes place.

At time t0 the velocity is = 1/t0 - 3

At time t1 the velocity is = 1/t1 - 3

The displacement is the average velocity between the two points, t0 and t1. This can be written as:

[(1/t1 - 3) + (1/t0 - 3)/\]/2

Displacement: s(t) = (t1 - t2)* [((1/t1 - 3) + (1/t0 - 3))/2]

The work done by stretching a certain spring increases by 0.13x joules per centimeter (where x is the displacement, in centimeters, beyond the spring's natural length). How much work (in Joules) must be done in order to stretch the spring from x?

Answers

Answer:

$W = 0.06\cdot (x_(f)^(2)-x_(o)^(2))$

Explanation:

The work done by stretching the spring is:

$W = 0.13\int\limits^{x_(f)}_{x_(o)} x\, dx$

$W = 0.06\cdot (x_(f)^(2)-x_(o)^(2))$

Explain why the current is reduced as electrons move through a conductor.

Answers

The current is reduced as less energy is available to move electrons through the wire.

This is because electrons moving through the conducting substance collide with the electrons and ions.

This causes collisions which further more convert kinetic energy into thermal energy because of the fewer energy that is available, it reduces.

Moreover the resistivity factor of the conductor it self might play some role and the loss of energy too.

as current moves through the conductor; the resistance of the conductor causes the original amount of current to reduce do to the length and the cross section size of the wire.

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