chanice drives her scooter 7 kilometres north. she stops for lunch and then drives 5 kilometres east. what distance did she cover? what was her displacement?/8

Answers

Answer 1

By using vector

a. the distance traveled is 12 kilometres

b. the resultant displacement is (7 i + 5 j) kilometres

We need to know about vectors to solve this problem. Vector has magnitude and also direction. Displacement is included in vector. It can be written as

s = sx i + sy j + sz k

where s is displacement, sx is displacement on x-axis, sy is displacement on y-axis and sz us displacement on z-axis.

From the question above, we know that

east = positive x

south = negative y

west = negative x

north = positive y

s1 = 7 j

s2 = 5 j

The distance traveled is

s = s1 + s2

s = 7 + 5

s = 12 kilometres

The resultant displacement is

s = s1 + s2

s = 7 i + 5 j

s = (7 i + 5 j) kilometres

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Related Questions

American football is played on a 100 yd long field, excluding the end zones. how long is the field in meters? (assume that 1 meter equals 3.281 feet.)

Answers

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

WILL GIVE BRAINLIEST

When you remove energy in a phase change what what happens to the kinetic energy?

Give and example of this type of phase change

explain the kinetic energy change from one phase to the other using movement of the molecules

Answers

Answer: chicken nuggy

Explanation:

because chicken muggy

(i) when vs 10 v with the switch on, what is the total charge q transported through rl in 2.5 seconds? (ii) when vs 15 v with the switch on, what is the energy w required to transport 0.5 (c) of charge through rl?

Answers

(i) when vs 10 v with the switch on, what is the total charge q transported through rl in 2.5 seconds?

(ii) when vs 15 v with the switch on, what is the energy w required to transport 0.5

The is 7.5 Joule.

The unit of energy in line with the metric device of devices (SI) is said to be the joule (J).

similarly, power is expressed non a extensive style of other SI-incompatible units. energy, ergs, kilowatt-hours, kilocalories, and British Thermal gadgets are some of these gadgets.

(i) v_s = 10 v when switch ON

q_0=0 [when switch off]

q=q_0+∫0-t i(t)dt

q=∫0-t=2.5sec i(t)dt

q= ∫0-t=sec 1mAdt

q=1×10^-3[t]0 - 2.5 sec

q=1×10^-3[2.5]

q=2.5×10^-3

q=2.5mC

(ii)

i=15/10=1.5mA

w=vit

q=0.5 column

q=q_0-0+∫0-t i(t)dt

q=∫ 0-t 1.5mAdt

q= 1.5×10^-3t

0.5= 1.5×10^-3t

t=0.5/ 1.5×10^-3t=(0.5/1.5)×10^3t

t=0.3333×10^3=333.3 second

w=vit

=15×1.5×10^3×0.3333×10^3

w=15×1.5×0.3333

w=7.49925

w=7.5 Joule

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Newton’s second law relates an object’s acceleration to its mass and the net force acting on it. Does newton’s second law apply to a situation in which there is no net force? select the best explanation.

Answers

No, the statement does not justify the situation because when the Net Force is 0 then it means that Inertia is greater than Force. So, it follows Newton's first law of Motion

The first law of motion which is often referred to as the 'Law of Inertia' states that an object tends to remain in the motion it's set in. If the object is set in motion it'll tend to be in motion or if the object is at rest then it'll tend to stay at rest. The object will only change its position when an external force is applied to it.

This tendency to remain in its state of motion is called 'Inertia' which acts as a resistance force when an external force is applied. If the magnitude of the external force is less than the Inertia object will not change its state of motion. So when the net force applied to an object is 0 the object will follow the Law of Inertia.

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A mass attached to a spring is displaced from its equilibrium position by 5cm and released. The system then oscillates in simple harmonic motion with a period of 1s. If that same mass–spring system is displaced from equilibrium by 10cm instead, what will its period be in this case?.

Answers

The period of the pendulum is √2 seconds.

We need to know about pendulum experiments to solve this problem. The pendulum is a simple experiment to calculate gravitational acceleration. The gravitational acceleration can be calculated by

g = 4π² . L / T²

where g is gravitational acceleration, L is the length of the string and T is the period.

From the question above, we know that:

T1 = 1 s

L1 = 5 cm

L2 = 10 cm

By using proportionality, the squared period is proportional to the length. Hence,

T² ~ L

Using the ratio, we can write

T1² / T2² = L1 / L2

1² / T2² = 5 / 10

1 / T2² = 1 / 2

T2² = 2

T2 = √2 second

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identify the conditions under which a given system of forces can be reduced to a single force. (check all that apply.)

Answers

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?

A force is a push or a pull on an object and it is a vector quantity.Therefore, it has both direction and magnitude.Force can cause a change in the velocity of an object.Friction is created because of the force.The formula of force is a product of mass and acceleration.

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.

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For a total trip of several hours duration, a ratio of the total distance traveled to the total time elapsed is a (an)?

Answers

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

What is the speed on average?

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.

What is the formula for average speed?

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

What is the SI unit of average speed?

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.

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a boy is to catch a ball which drops vertically from the top of a 14.9-m tower. find the average velocity at which the boy, initially 6.62 m from the base of the tower,

Answers

The velocity of the boy in order to catch the ball is 3.8 m/s.

Time of motion of the ball

The time taken for the for the ball to fall from the given tower is calculated as follows;

t = √(2h/g)

where;

h is the height of fall of the ballg is acceleration due to gravity

t = √(2 x 14.9 / 9.8)

t = 1.74 seconds

Velocity of the boy

The velocity of the boy in order to catch the ball is calculated as follows;

x = Vxt

Vx = x/t

Vx = 6.62 m / 1.74 s

Vx = 3.8 m/s

Thus, the velocity of the boy in order to catch the ball is 3.8 m/s.

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Compare your power output both climbing and running up the stair way to a 60- wattslight bulb?

Answers

Running up the flight of stairs produces more horsepower than strolling up them does. because running causes you to go through energy more quickly.

Work (in joules) equals your weight (in newtons) times the staircase's height (in meters.) The power you now possess is equal to the sum of the labor you completed and the time it took, or: Work (in joules) divided by time equals power (in watts) (in seconds.) The college alumnus questionnaire's physical activity index (PAI) is calculated on the basis of the assumption that every 20 steps is equivalent to 8 kcal of energy expenditure. This amount equates to a 0.40 kcal energy cost. You put in the same amount of effort as your potential energy changes.

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A system gains 747 kj of heat, resulting in a change in internal energy of the system equal to 176 kj. how much work is done? = kj

Answers

A system gains 747 kJ of heat, resulting in a change in internal energy of the system equal to 176 kJ, here -571 kJ of work has been done.

Explanation

Using the  First law of thermodynamics

ΔU = q + w

Here Change in internal energy ΔU = 176 kJ

And Heat gained by the system (q) = 747 kJ

With Work done being w

So, apply the formula in the given information we get

176 kJ = 747 + w

w = 176  - 747 kJ

    = -571 kJ

Here, the negative symbol denotes that the work has been done.

What is thermodynamics?

The study of how heat and other types of energy interact is the subject of the physics field known as thermodynamics. The effects of thermal energy on matter are specifically discussed, as well as how thermal energy is changed into and out of other types of energy.

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alex goes cruising on his dirt bike. he rides 700 m north, 300 m east, 400 m north, 600 m west, 1200 m south 300 m east and finally 100 m north. what distance did he cover? what was his displacement? (use 1cm

Answers

He started from point O . After traveled he reached at the same point O.

from the graph given which is attatched :

OA = 700m ab = 300 m bc = 400m

CD = 600m DE = 1200m EF = 300m and FO = 100m

total distance covered =  700+ 300 + 400 + 600 + 1200 + 300 + 100

= 3600m

hence he covered 3600m distance

since, he started from point O and after travelled he reaches the same point from where he started means the initial and final position is same

therefore the total displacement is zero

displacement = 0

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Two trains are 150 km apart. train a moves at 50.0 km/hr towards train b, which moves at 30.0 km/hr toward train a on the same track. how much time do they have before the trains collide?

Answers

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.

What is relative motion, and why is it considered important?

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.

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A wave moves along a slinky with a speed of 0.75 m s1.
The wave travels the full length of the slinky in 3.2 s.
Calculate the length of the slinky.

Answers

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.

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Can you someone me I’m stuck on this question

Answers

Velocity

Speed is a description of how fast an object moves; velocity is how fast and in what direction it moves. In physics, velocity is speed in a given direction. When we say a car travels at 60 km/h, we are specifying its speed. When we say a car moves at 60 km/h to the north, we are specifying its velocity.

A boy weighs 400 N. What is his mass?

Answers

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).

What do you observe when you switch on your light source and hold your largest plastic shopping bag square between the light source and the wall?

Answers

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.

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At a distance of 10 km from a point source (isotropic) radio transmitter, the amplitude of the e-field is 0.20 volts/meter. what is the total power emitted by the radio transmitter?

Answers

The total power emitted by the radio transmitter is 6.67×[tex]10^{4}[/tex]W .

What is a transmitter?

The given parameters;

amplitude of the electric field, E = 0.2 V/m

distance of the transmitter, = 10 km = 10,000 m

The intensity of the radio wave from the transmitter is calculated as follows

[tex]I=E^{2}[/tex]/μc

I = [tex]5.305[/tex]×[tex]10^{-5}[/tex] [tex]W/m^{2}[/tex]

The total power emitted by the radio transmitter is calculated as follows;

I= P/A

P= IA

P = 6.67×[tex]10^{4}[/tex]W.

A radio transmitter, often known as a transmitter, is an electronic device used in electronics and telecommunications that uses an antenna to emit radio waves. A radio frequency alternating current is produced by the transmitter and applied to the antenna. The antenna emits radio waves after being stimulated by this alternating current.

All radio-communicating electronic devices, including radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, Bluetooth-enabled gadgets, garage door openers, two-way radios in aircraft, ships, and spacecraft, radar systems, and navigational beacons, require transmitters as essential component parts.

A transmitter could be a standalone electronic device or an electrical circuit housed inside another electronic gadget.  

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rolls of foil are 304 mm wide and 0.020 mm thick. (the density of foil is 2.7 g/cm3 .) what maximum length of foil can be made from 1.09 kg of foil?

Answers

The maximum length of foil will be 6639.8635 cm or 66.3986 m

To find the maximum length of the foil, the given datas are:

Width of roll of foil = 304 mm

Height or thickness = 0.020 mm

Density of foil = 2.7 g/cm³

Mass of foil = 1.09 Kg

What is Density?

Density is the substance's  mass per unit volume. It can be also described by measuring how the particles in the substances tightly packed together.

d = m/ v

v = length (l) × width (w) × height (h)

First of we will convert the Kg into gram and mm into cm.

For 1 Kg = 1000 g

1.09 × 1000 = 1090 g

For 1 cm = 10 mm

304 / 10 = 30.4 cm

0.020 / 10 =  0.0020 cm

Now we will put the values in formula:

d = m/ l× h× w

l = m / d × h× w

l = 1090 g / 2.7 g/cm³× 30.4 cm × 0.0020 cm

l = 1090 g/ 0.16416 g/cm

l = 6639.8635 cm or 66.3986 m

The maximum length of foil will be 6639.8635 cm or 66.3986 m

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Which two activities are normally controlled by the northbridge part of the chipset?

Answers

RAM, video card, are the two activities normally controlled by the northbridge part of the chipset.

The Northbridge chipset generally controls access to the RAM, video card, and the speeds at which the CPU can communicate with them. Northbridge is an Intel chipset that communicates with the computer processor and controls interaction with memory, the Peripheral Component Interconnect (PCI) bus, Level 2 cache, and all Accelerated Graphics Port (AGP) activities.

There are two activities that are normally controlled by the Northbridge part of the chipset. These include having access to the RAM and video card. To understand the Northbridge, you must understand part of it is used to be the memory controller chip used to retrieve memory from RAM for the LPU.

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Recoil is noticeable if we throw a heavy ball while standing on roller skates. If instead we go through the motions of throwing the ball but hold onto it, our net recoil will be?.

Answers

Answer:

zero

Explanation:

Determine the average speed in m/s of a hockey puck that takes 15 seconds to move 90.0 meters.

Answers

Explanation:

average speed= total distance/total time

=90÷15

=6

a wheel with a radius of 45.0 cm rolls without slipping along a horizontal floor (fig. 3-37). at time t1, the dot p painted on the rim of the wheel is at the point of contact between the wheel and the floor. at a later time t2, the wheel has rolled through one-half of a revolution. what are (a) the magnitude and (b) the angle (relative to the floor) of the displacement of p?

Answers

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

displacement is change in position is determined by the distance and direction of an object from the starting point to the ending point. and shown by displacement vector

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You run around neyland stadium. when you are halfway around the stadium, which value cannot be 0?
a) instantaneous speed
b) average speed
c) instantaneous acceleration
d) average acceleration

Answers

When you are halfway around the stadium, average speed value cannot be 0.

Average speed = Total distance travelled / Time taken.

Since you ran halfway across the stadium, a certain amount of distance has been covered. The only way the average speed can be zero is if you remained stationary over a given interval of time.

In a distance-time graph, at the halfway point in the stadium, slope is equal to zero. So, Instantaneous speed is zero. In a Velocity-time graph, at the halfway point in the stadium, slope is equal to zero. So, Instantaneous acceleration is zero. In a Velocity ( w.r.t. time )-time graph, at the halfway point in the stadium, slope is equal to zero. So, Average acceleration is zero.

Therefore, when you are halfway around the stadium, average speed value cannot be 0.

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When a transverse wave travels through a medium, which way does matter in the medium move?

Answers

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.

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A catapult can project a projectile at a speed as high as 37.0 m/s. If air resistance can be ignored, how high (in m) would a projectile launched at this speed rise if projected straight up?

Answers

The height of the projectile is 69.7 meters when air resistance can be ignored.

The initial speed (u) of the projectile is = 37 m/s

The final speed (v) is 0 because, at a high point, the projectiles come at the rest condition.

The acceleration is negative when the project is thrown in an upward direction. Therefore, the acceleration is, a = -g

Or, a = -9.81 m/s²

Now, by using the kinematics equation, we can find the height of the projectile.

v² = u² + 2gh

(0 m/s)² = (37 m/s)² + 2(-9.81 m/s²)h

2(9.81 m/s²)h = (37 m/s)²

Or, h =  (37 m/s)²/ 2(9.81 m/s²)

Or, h = 69.7 m

Therefore, the height of the projectile is 69.7 meters.

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If membrane potential is greater than equilibrium potential, then driving force is __

Answers

Then driving force for the membrane is hyperpolarized.

What is equilibrium potential?

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.

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Sodum has a work function of 2. 1eV and is illuminated by radiation whose wavelength the is 150mm, Calculate the maximumum energy.​

Answers

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

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if the electric field is suddenly turned off, what is the speed of the sphere at the bottom of its swing (in m/s)?

Answers

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

  =   (2.OO x10^-3  × 9.80 ) ÷ (1000 NfC)tan 13.4°

= 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

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four point charges, each of magnitude 9.66 µc, are placed at the corners of a square 87.1 cm on a side. if three of the charges are positive and one is negative, find the magnitude of the force experienced by the negative charge. the value of coulomb’s constant is 8.98755 × 109 n · m2 /c 2 .

Answers

The magnitude of the force experienced by the negative charge is 0.198N.

The Coulombs law is an expression that states that  magnitude of the force between two charges q and Q separated by a distance r is given by

F=k|Q|q|r2

where k is Coulomb constant.

Answer and Explanation:

Let us visualize corners of the square as four points on the xy-axis. The four points would be origin (0,0), then (78.9 cm, 0), then (0, 78.9 cm) and (78.9 cm, 78.9 cm). These points are corners of the square described in the question. Let  negative charge be at origin. Let charge 1 be located at (78.9 cm, 0), that is, its located along x-axis, a distance 78.9 cm away from the negative charge. The force due to this charge 1 acts in positive x-direction as the two charges attract. Let charge 2 be at point (0, 78.9 cm) and the force due to this charge acts in the positive y-direction. Charge 2 is also 78.9 cm away from negative charge. Let charge 3 be located at point (78.9 cm, 78.9 cm). Force due to this charge has the x and y-components. The angle this force makes with positive x-axis is 45 degrees since this is a square. The distance between charge 3 and negative charge is

√(78.9cm)2+(78.9 cm)2 =111.5814501cm.

Now we can calculate force on the negative charge due to each individual positive charge. Force due to the charge 1 is [tex]F_{1} =k|+q||-q| r^{2}(8.98755*109N.m^{2}/C^{2})*(2.68*106)*(2.68*106)^{2}(0.789m)^{2} =0.1036947816N[/tex]

in positive x-direction. Force due to the charge 2 has same magnitude as force due to charge 1, but acts in the positive y-direction.

F2 =0.1036947816N

The force due to the charge 3 is

[tex]F_{3}=k|+q||-q| r^{2} =(8.98755*109N.m^{2}/C^{2})*2.68*10^{-6} )^{2}(1.115814501m)^{2}= 0.05184739076N[/tex]

The x and y-components of force due to charge 3 are

F3,x=F3cos45=(0.05184739076√22)N=0.03666164159N

in positive x-direction, and

F3,y=F3sin45=(0.05184739076√22)N=0.03666164159N

in positive y-direction.

Therefore, x-component of the resultant force experienced by the negative charge is

Fx=F1+F3,x=0.1036947816N+0.03666164159N=0.1403564232N

and y-component is

Fy=F2+F3,y=0.1036947816N+0.03666164159N=0.1403564232N

Therefore, magnitude of the force experienced by the negative charge is

[tex]F= \sqrt{Fx_{2}+F_{2y} }= \sqrt{(0.1403564232N)^{2}+(0.140356432N)^{2} } =0.198493973N[/tex] =0.198N

correct to the three significant figures.

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Let v = (2, 3, 1), w = (1, 1, 1), and 3u 2v 4w = (1, 2, 3). find (a) the vector u (b) the linear combination: 2u 3v 5w.

Answers

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.

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