at what speed would an 6.90–kg trash can have the same momentum as the truck? (note that the speed is unreasonable.)

The vector of linear combination = u is -7/3 i - 8/3 j - k , a) linear combination is xi + yj + zk = (1/3) (-7i -8j-3k) b ) linear combination is 19/3 i + 17/3 j + 6 k

The vector u is  [tex]-7/3[/tex] i - [tex]8/3[/tex] j - k.

The linear combination 2u + 3v + 5w  is 19/3 i + 17/3 j + 6k.

in line with the posed question.

v = (2, 3, 1)

w = (1, 1, 1)

And

3u + 2v + 4w = (1, 2, 3)

From,

v = (2, 3, 1)⇒ v = 2i + 3j + 1k

w = (1, 1, 1)⇒ w = I + j + j

Evaluation :

a). Let u be the vector xi + yj + zk.

Here,

3u + 2v + 4w = (1, 2, 3)

I + 2j + 3k = 3u + 2v + 4w

I + 2j + 3k = 3(xi + yj + zk) + 2(2i + 3j + k) + 4(i + j + k)

I + 2j + 3k = 3xi + 3yj + 3zk + 4i + 6j + 2k + 4i + 4j + 4k

I + 2j + 3k = 3xi + 3yj + 3zk + 8i + 10j + 6k

I + 2j + 3k - 8i -10j -6k = 3xi + 3yj + 3zk

-7i -8j -3k = 3xi + 3yj + 3zk

xi + yj + zk = (1/3) (-7i -8j-3k)

b). The linear combination

2u + 3v + 5w

= 2(-7/3i -8/3j - k ) + 3(2i + 3j + k) + 5(i + j + k)

= -14/3 i -16/3j -2k + 6i + 6j + 3k + 5i + 5j + 5k

= -14/3 i -16/3j -2k  + 11i + 11j + 8k

= 19/3 i + 17/3 j + 6k

What is a linear combination of a vector?

A linear combination is  of two or more vectors in which the vector obtained by adding two or more vectors (with different directions) which are then  multiplied by scalar values.

To learn more vector and linear combination about from the given link:

brainly.com/question/12505220

#SPJ4

Answer:

100 yd * 3 ft/yd / 3.281 ft/m = 91.4 m

Check" 91.4 m " 3.281 ft/yd = 299.9 ft = 100 yd

While an object moves along a curved path it is not possible for acceleration to be zero.

The term acceleration has to do with the change of velocity with time. We know that velocity is a vector quantity. Since velocity is a vector quantity, it means that velocity would have both magnitude and direction.

Given the fact that the magnitude of the velocity of the object that is moving along a curved path may be constant, the direction of the velocity still changes.

Owing to the fact that we must consider both changes in magnitude and direction of velocity, it then follows that while an object moves along a curved path it is not possible for acceleration to be zero.

Learn more about acceleration:https://brainly.com/question/12550364

#SPJ1

The average velocity for the time interval from 2.10 s to 2.85 s is Vavg = 18 m/s.

What is  average velocity?

A vector quantity is average velocity. The change in position or displacement (∆x) divided by the time intervals (∆t) during which the displacement happens is the definition of average velocity. Depending on how the displacement is spelled out, the average velocity might be either positive or negative.

Vavg = d X/ d T

Here d X = change in distance

and d T = change in time

there Therefore    dT= 2 x 9 x t

so, at t= 2.10s x = 37.8 m/s

at t= 2.85s  x= 51.3 m/s

Therefore     Vavg = (51.3 m/s - 37.8 m/s) / ( 2.85s - 2.10s )

Vavg = 18 m/s

To learn more about average velocity click on the link below:

https://brainly.com/question/23856383

#SPJ4

Answer:

A. Her distance is 4 miles.

B. Her displacement is positive.

Explanation:

She traveled 2 miles and then 2 miles so 2 + 2 = 4.

Displacement is the change in direction but she didn't change direction and continued in the same direction so the displacement would be positive.

Answer: chicken nuggy

Explanation:

because chicken muggy

The horizontal distance is equal to the half of the circumference of wheel.

x = 2 πr/2

= πr

= 3.14 * 45 * 10^-2

=1.413m

The vertical distance is equal to the diameter of wheel.

y=2r

= 2 * 45 * 10^-2

= 0.9m

The magnitude of the displacement of P is,

r^2 = x^2 + y^2

r^2 = (1.413)^2 + ( 0.9m)^2

r = 1.675

the angle is  tanθ

 θ= 32.5

To know more about displacement   visit : https://brainly.com/question/11934397

#SPJ4

[tex]y = d \times sin \alpha \\ y = 13.04 \times sin3 \\ y \approx8.028 \: meters[/tex]

Two nonnegative real numbers with a sum of 46 that have the largest possible product is 23 and 23.

Explanation

Any no's half when multiplied by itself gives the larges possible outcome also being the sum of the given no. as 46

Some trials

23 + 23 = 46        ,       23 × 23 = 529

22 + 24 = 46        ,       22 × 24 = 528

21 + 25  = 46        ,        21 × 25 = 525

Hence, proven that Any no's half when multiplied by itself gives the larges possible outcome also being the sum of the given number.

Any number that exists in the physical universe is a real number. Everywhere we look, we see numbers. Natural numbers are used to count things, while rational numbers are used to represent fractions,

irrational numbers are used to calculate a number's square root, integers are used to measure temperature, and so on. A group of real numbers is created by these various kinds of numbers.

Learn more about real number

https://brainly.com/question/17201233

#SPJ4

A ferris wheel having a radius of 8 m has a velocity of 8 m / s. is there a danger of the riders flying off .  No, the ferris wheel is not moving too fast.

What is a velocity?

Velocity may be a vector quantity that refers to "the rate at which an object changes its position." Imagine an individual moving rapidly - one step forward and one step back - always returning to the original starting position. While this might end in a frenzy of activity, it might result in a zero velocity.

What is the two types of velocity?

Constant velocity: is that the speed at which an object travels equal displacements in equal times. Variable velocity: it's the speed at which an object cuts different displacements at different times.

Learn more about velocity:

brainly.com/question/25749514

#SPJ4

If both the mass of a simple pendulum and its length are doubled the period will The time period of a pendulum does not depend on the mass of bob. So if the mass of bob doubled, the time period remains the same

A weight suspended from a pivot such that it can freely swing is called a pendulum. Gravity's restoring force will cause a pendulum to accelerate back toward its equilibrium position if it is sideways moved from its resting, equilibrium position. When the pendulum is freed, the restoring force acting on its mass causes it to oscillate, swinging back and forth, about its equilibrium point. The period is the length of time needed for one full cycle, or a left swing and a right swing. The period is influenced by the pendulum's length and, to a lesser extent, by the amplitude, or swing's width

To learn more about simple pendulum:

https://brainly.com/question/14759840

#SPJ4

The angular acceleration of the tyres is -4.213 rad/[tex]s^{2}[/tex] .

Here we have to use the third equation of motion in case of rotational motion so as to calculate the angular acceleration of the tires. It is given by

[tex]w\w\limits^2_f =w\w\limits^2_i + 2\alpha \theta[/tex]

Then, converting the transitional velocity to rotational velocity,

vi = 95km/hr = 95 x 5/18 m/s = 26.39 m/s

vf = 55 km/hr = 55 x 5/18 m/s =15.28 m/s

Diameter of tire = 0.80m

Radius of tire = Diameter of tire/2 = 0.80/2 = 0.40m

Therefore,

wi = [tex]\frac{vi}{r}[/tex] = 26.39/0.40 rad/s = 65.98 rad/s

wf = [tex]\frac{vf}{r}[/tex] = 15.28/0.40 rad/s = 38.20 rad/s

[tex]\theta[/tex] = 65 revolutions= 2[tex]\pi[/tex] x 65 = 408.40 radians

so we have,

[tex]\alpha[/tex] = [tex]\frac{w_{f}^2 - w_{i}^2 }{2 \theta }[/tex] = [tex]\frac{38.20^2 - 65.98^2}{2*408.4}[/tex]=  -4.213 rad/[tex]s^{2}[/tex]

Hence the angular acceleration of the Tyres is -4.213 rad/[tex]s^{2}[/tex].

To know more about rotational velocity, visit:

https://brainly.com/question/26095104

#SPJ4

Answer:

The wave takes 3.2 s at 0.75 m s⁻¹ to travel across a slinky. The length of slinky is 2.4 m.

What is a wave?

A wave is defined as a disturbance that travels from one spot to another through a medium. As an example of a wave, consider a slinky wave. When stretched from end to end and maintained at rest, the slinky assumes a natural state known as the equilibrium or rest position. The slinky's coils automatically assume this posture, equally spaced apart. The initial particle is pushed or shifted from its equilibrium or rest state to introduce a wave into the slinky.

Explanation:

As we know, [tex]speed=\frac{distance}{time}[/tex]

Therefore, [tex]distance = speed[/tex] × [tex]time[/tex]

=> d = 0.75 x 3.2

       = 2.4 m

Hence, the distance the wave travels or the length of the slinky is 2.4 m.

To know more about waves, click on the link

https://brainly.com/question/10750459

#SPJ9

Two trains are seen as 150 km apart, if they are moving towards each other, they have 1.875 hours before the two trains collide.

The motion or the speed of any object present with relation to a certain point is referred to as relative motion. For instance, a ball thrown upward while in a moving object, like a bus, would be travelling at the same speed with respect to the bus, and would fall again in relation to that speed.

The same physical rules that govern objects at rest on the planet also govern objects in any reference frame that is moving relative to the earth at a constant speed.

The Initial position of Train A = 0 km

The Initial position of Train B = 150 km

x= xi + vi*t

We have to set them equal to each other to find when their positions are the same.

50t = -30t + 150

t = 1.875 hr.

To know more about relative motion visit:

https://brainly.com/question/15836528

#SPJ4

If an object from a tall building falls, it will take it 4.995 seconds to reach a speed of 49 m/s.

The time taken for an object to fall can be calculated using the following equation of motion:

V = u + at

Where;

According to this question, an object from a tall building falls. The time it would take to reach a speed of 49m/s can be calculated as follows:

49 = 0 + 9.81(t)

49 = 9.81t

t = 49/9.81

t = 4.995s

Therefore, if an object from a tall building falls, it will take it 4.995 seconds to reach a speed of 49 m/s.

Learn more about time in motion at: https://brainly.com/question/15080570

#SPJ1

Einstein’s understanding of curved space-time helped him understand gravity better on Earth.

The man Albert Einstein was the person who first brought up the idea of relativity. The relativity theory drove home the assertion that there are no absolutes in the universe.

On the other hand, the works of Aristotle and Newton about gravity did not include this element of relativity. Though the work of Newton was highly empirical, the results did not incorporate the ideas of relativity.

Thus, what distinguishes Einstein from Newton and Aristotle is Einstein’s understanding of curved space-time helped him understand gravity better on Earth.

Learn more about Albert Einstein:https://brainly.com/question/1275198

#SPJ1

When we set the object adjacent to the flashlight and not exactly into its beam of light, we probably won't initially notice a shadow.

However, if we place the object directly in the path, we should be able to see a shadow of it on the wall.

What is shadow?

A shadow, or black place, is produced whilst an opaque item deflects light from a mild source. at the back of a light-emitting gadget, it fills the whole three-dimensional area. A 2-D backward projection of the object obstructing the mild may be used to conceptualise the cross section of a shadow.

mild goes in a directly line, therefore setting an object subsequent to a flashlight however out of the mild's direct route prevents us from seeing a shadow. because the object became out of the mild's direct direction, it was not able to block the light from the flashlight's source.

To learn more about shadow refer the link:

https://brainly.com/question/922673

#SPJ4

The condition under which a system of forces is reduced to a single force is - One can replace the force - couple system at O by a single force R acting along a new line of action if R and vector M₀ are mutually perpendicular.

What is a force?

Hence, the only condition is if R and vector M₀ are mutually perpendicular, then the system of forces can be reduced to a single force.

To learn more about force, visit: https://brainly.com/question/17646386

#SPJ4

True, A longitudinal design can often determine cause and effect more accurately than any cross-sectional design and this is a proven case.

By virtue of its scope, a longitudinal study is more likely than a cross-sectional study to suggest cause-and-effect linkages. In general, the design should be influenced by the research.

Sometimes, the direction of the research helps determine which design is most appropriate.

In contrast to longitudinal designs, adopting cross-sequential designs gives researchers the opportunity to quickly analyze a variety of age groups.

It also allows researchers to test for cohort effects, which is frequently impossible in a conventional longitudinal design.

A cross-sectional investigation when is carried out using several samples. The identical sample is used for longitudinal research.

To know more about Longitudinal waves, visit:

https://brainly.com/question/8497711

#SPJ4

v = 1.24 m/s

The net force on the sphere along x  axis direction is zero so,

∑fx = 0

T sineθ  = qE

The net   force on the sphere along y aixs direction is  zero so,

∑fy = 0

T cosθ  = mg

From the above two  equations, we got

tan θ =qE÷mg

The charge on the sphere is

q = mg ÷ E tan θ

= 82.27 micro coloumb

so, now The speed of the sphere at the bottom is

v = [tex]\sqrt{x} 2gl(1-cos\theta )[/tex]

v= [tex]\sqrt{x} 2( 9.8)(0.23)(1-cos13.4)[/tex]

v = 1.24 m/s

To know more about  force   visit : https://brainly.com/question/13191643

#SPJ4

The displacement is 900 meter current to the South.

We know that velocity is the ratio of the displacement of a body to time. Displacement is a vector quantity just as velocity. We know that given the fact that velocity and displacement are vectors, the direction of the movement is very important.

Thus, we can see that;

Velocity =  3 meter/sec  current to the South

Time = 5 minutes or 300 sec

Velocity = displacement/ time

displacement = velocity * time

displacement = 3 meter/sec  current to the South *  300 sec

= 900 meter current to the South

Learn more about velocity:https://brainly.com/question/18084516

#SPJ1

Answer:

40kg(88pounds)

Explanation:

.

.

.

.

.

.

Answer: ≈ 40.8 kilograms (89.9 pounds)

Explanation: Well, assuming the boy is on Earth, then the gravitational acceleration is approximately 9.8 m/s^2.

So, we get: mass = weight / gravitational acceleration

Put two and two together and you get 400-N / 9.8 m/s^2 ≈ 40.8 kg (89.9 pounds).

Answer: The resultant is the vector sum of two or more vectors.

The correct answer is 4.

We know that, for an ideal, mono atomic gas, we have:

Temperature is directly proportional to Kinetic Energy

Kinetic Energy = 1/2 x m x v^2, where

m - mass of the gas

v - velocity of the gas

Thus, temperature is directly proportional to the square of the velocity of the gas.

Therefore, if velocity (or speed) becomes twice, the Kelvin temperature will become four times of its original value.

If velocity of all the atom is doubled , then root mean square velocity will also get doubled .

Also we know , root mean square velocity Vrms = v(3RT/molar mass )

So  Vrms is directly proportional to square root of T (temperature )

So is Vrms gets doubled , temperature  gets 4 times .

To learn more about monatomic ideal gas refer the link:

https://brainly.com/question/12370781

#SPJ4

A transverse wave is one in which the motion of the medium's particles is perpendicular to the wave's direction of propagation.

A wave is a dynamic disturbance of one or more quantities that propagates through time. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.

It is a mechanical wave that conveys kinetic energy through the movement of the particles affected when a wave moves a particle of matter. The behavior of the wave's particles sometimes referred to as the oscillation of the wave, is used to categorize different types of mechanical waves.

The movement of the medium's particles as a transverse wave travels through it is side-to-side and perpendicular to the wave's direction of travel. Any direction in relation to up and down is acceptable as long as it creates a line of motion that is perpendicular to the direction of travel.

Learn more about transverse waves here:

https://brainly.com/question/15531840

#SPJ9

The magnitude of the magnetic field inside the toroid varies as a function of :

[tex]B=\mu _0 nI[/tex]

where, B = magnetic field

n is the number of turns,

I is the current induced

What is a toroid?

To learn more about Toroid, refer to:

brainly.com/question/15842779

#SPJ4

For a total trip of several hours' duration, a ratio of the total distance traveled to the total time elapsed is average speed.

The overall distance that is covered by an object in a given amount of time is its average speed. In essence, average speed serves as a tool for calculating the rate of travel time and distance.

The average speed is a scalar quantity.

It is represented by magnitude and lacks direction. The formula for an object’s general average speed is given as follows:

[Average Speed = The Total Distance Traveled / The Total Time Taken

The SI unit for the average speed is m/s.

Meter per second

The S.I. speed unit is the meter per second. Additionally, speed is expressed in kmph or that can be said as kilometers per hour.

To know more about average speed visit:

https://brainly.com/question/12322912

#SPJ4

The maximum energy is 6.2 eV.

Photoelectric effect: Some electrons are released from the metal surface when photons strike it. The photoelectric effect is the name given to this occurrence.

The work function (φ) of a metal is the minimal amount of energy required to remove electrons from its surface.

Maximum kinetic energy is the most energy that electrons have when they are expelled off a metal surface (KEmax).

The work function of sodium is 2.1 eV.

The wavelength of the radiation is 150 nm.

Work function, φ = 2.1 eV

Wavelength, λ = 150 nm = 150 × 10⁻⁹ = 15 × 10⁻⁸ m

Einstein's photoelectric equation is given as:

E = φ + KE(max)

KE(max) = E - φ

KE(max) = ( hc / λ ) - φ

KE(max) = ( 6.63 × 10⁻³⁴) × 3 × 10⁸ / (15 × 10⁻⁸ × 1.6 × 10⁻¹⁹) - 2.1

KE(max) = 0.8287 × 10 - 2.1

KE(max) = 8.3 eV - 2.1 eV

KE(max) = 6.2 eV

Learn more about wavelength here:

https://brainly.com/question/10750459

#SPJ9

Then driving force for the membrane is hyperpolarized.

The electrical potential difference across the cell membrane that exactly balances the ion concentration gradient is known as the equilibrium potential. Since the system is in equilibrium, the membrane potential will normally stay at the equilibrium potential.

Additionally, the equilibrium potential for a group of ions in a membrane provides us with a baseline for how this membrane is operating or behaving in a given situation where it is not at rest.

to learn more about equilibrium potential go to -

https://brainly.com/question/28304088

#SPJ4