Find the direction of the sum of
these two vectors:

Answer:

c: long and thin resistor.

Explanation:

The resistance of a resistor is given by:

R = ρ*L/A

where:

R = resistance

ρ = resistivity (depends on the material)

L =  length of the material

A = cross-sectional area of the material

We can see that the length is on the numerator, which means that if we increase the length, then the resistance is increased.

We also can see that the cross-sectional area is on the denominator, then if we increase the area (for example, with a ticker resistor) the resistance decreases.

Then if we want to maximize the resistance, we need to have a long and thin resistor, so the correct answer is c.

Answer:

An atom is the smallest part of an element by itself, while molecules are built of multiple atoms.

A rainbow is produced by the combined effects of refraction, dispersion, and internal reflection of sunlight within water droplets in the atmosphere. The correct option is D.

When sunlight passes through water droplets suspended in the air, the light is refracted, or bent, as it enters and exits the droplets. This refraction causes the different colors of light to separate due to their varying wavelengths, a phenomenon known as dispersion.

Additionally, once inside the droplets, the light undergoes multiple internal reflections before finally exiting. These reflections further separate the colors and contribute to the formation of the rainbow.

Therefore, option d, which includes refraction, dispersion, and internal reflection in water droplets, is the correct explanation for the production of a rainbow.

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The maximum tοrque exerted by the persοn is 86.6 Nm.

Tοrque is a measure οf the tendency οf a fοrce tο rοtate an οbject arοund a specific axis. It is alsο referred tο as the mοment οf fοrce.

Given:

Mass οf the persοn (m) = 52 kg

Radius οf the circle fοrmed by the pedals (r) = 17 cm = 0.17 m

Weight οf the persοn (W) = m * g, where g is the acceleratiοn due tο gravity (apprοximately 9.8 m/s²)

Tο find the fοrce exerted by the persοn οn each pedal, we can use the equatiοn:

Fοrce (F) = Weight (W)

The weight οf the persοn is given by:

W = m * g

Substituting the given values:

W = 52 kg * 9.8 m/s²

W ≈ 509.6 N

Nοw, the maximum tοrque (τ) can be calculated using the equatiοn:

Tοrque (τ) = Fοrce (F) * Lever Arm (r)

τ = F * r

Substituting the values:

τ = 509.6 N * 0.17 m

τ ≈ 86.6 N·m

Therefοre, the maximum tοrque exerted by the persοn is apprοximately 86.6 N·m.

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Answer:

the correct one is 2

Explanation:

The emission and arcion spectra are similar, in the emission spectra a heated material emits photons for the internal transitions of the electrons, in the absorption spectrum the continuous emission of a lamp is absorbed at the energies that the material has transitions.

In our case the material is low early, so all the electrons are in their base states.

As the light beam has all wavelengths, those corresponding to the first emission of the material will be observed.

When reviewing the answers, the correct one is 2

Consider increasing the mass vibrating on a spring's oscillation's amplitude. The claims (A) and (D) regarding this mass are true.

A. Its maximum speed increases.

D. Its maximum kinetic energy increases.

Here is the explanation :

When you increase the amplitude of oscillation of a mass vibrating on a spring, two correct statements about the mass are:

A. Its maximum speed increases: The maximum speed of the mass occurs at the amplitude of the oscillation. Increasing the amplitude means the mass travels a greater distance from the equilibrium position, leading to a higher maximum speed during its oscillation.

D. Its maximum kinetic energy increases: The kinetic energy of the mass is directly proportional to the square of its speed. As the maximum speed increases, the maximum kinetic energy also increases because kinetic energy is dependent on the square of the speed.

The other two statements are incorrect:

B. Its period of oscillation does not change: The period of oscillation is determined by the properties of the spring and the mass and is independent of the amplitude. Increasing the amplitude does not affect the period of oscillation.

C. Its maximum acceleration does not change: The maximum acceleration of the mass occurs at the extreme points of its motion, which are determined by the properties of the spring and the mass. Increasing the amplitude does not change the maximum acceleration.

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Complete question :

Suppose you increase the amplitude of oscillation of a mass vibrating on a spring. Which of the following statements about this mass are correct? (There may be more than one correct choice.)

A. Its maximum speed increases.

B. Its period of oscillation increases.

C. Its maximum acceleration increases.

D. Its maximum kinetic energy increases.

Answer:

D

Explanation:

In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.

a) The angular acceleration of the wheels is approximately 0.861 rad/s². b) The angular velocity of the wheels after 18.0 s is approximately 15.5 rad/s. c) The cyclist has traveled approximately 201.06 meters in 18.0 seconds.

Time (t) = 18.0 s

Number of revolutions (N) = 89

Radius of the wheel (r) = 36.0 cm = 0.36 m

a) The angular acceleration (α) can be calculated using the formula

α = (2πN) / t²

where N is the number of revolutions and t is the time.

α = (2πN) / t²

α = (2π × 89) / (18.0²)

α ≈ 0.861 rad/s²

b) The angular velocity (ω) can be calculated using the formula

ω = αt

ω = αt

ω = 0.861 * 18.0

ω ≈ 15.5 rad/s

c) The distance traveled by the cyclist can be calculated using the formula:

distance = circumference of the wheel × N

where N is the number of revolutions and the circumference of the wheel can be calculated as 2πr, where r is the radius of the wheel.

Distance = circumference of the wheel × N

Distance = (2π × 0.36) × 89

Distance ≈ 201.06 m

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Answer:

El peso de la pieza dentro de la glicerina es 64.93 N.

Explanation:

El principio de Arquímedes nos indica que “todo cuerpo sumergido dentro de un fluido experimenta una fuerza ascendente llamada empuje, equivalente al peso del fluido desalojado por el cuerpo”.

Entonces, el peso del cuerpo dentro del fluido (peso aparente) será igual al peso real que tenía fuera de él (peso real) menos el peso del fluido que desplaza al sumergirse (peso del fluido o fuerza de empuje). Matemáticamente se expresa como:

Paparente=Preal−Pfluido

El peso del fluido desplazado o fuerza de empuje ejercida por el líquido está dada por la expresión:

Pfluido = ρliq • Vcpo • g

en donde:

Entonces, en este caso:

Paparente= 80 N - 1200 [tex]\frac{kg}{m^{3}}[/tex]* 0.001280 m³* 9.81 [tex]\frac{m}{cm^{2} }[/tex]

Resolviendo:

Paparente= 64.93 N

El peso de la pieza dentro de la glicerina es 64.93 N.

An intensity level of 10^11 times the threshold of hearing (1 x 10-12 W/m2) corresponds to a decibel rating of 110 db.

What decibel level does a whisper have?

The volume of a sound is measured in decibels (dB), with a whisper being between 20 and 30 dB, boisterous conversation being around 50 dB, a vacuum cleaner being around 70 dB, a lawn mower being around 90 dB and an automobile horn at one metre being around 110 dB. Decibels are units used to measure sound volume.

An intensity level of 10^11 times the threshold of hearing (1 x 10-12 W/m2) corresponds to a decibel rating of 110 db. Thus, the intensity is 0.1 W/m2 at a distance of 2.0 m from the speaker.

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To achieve a 3.6-times magnified virtual image, you will need a concave mirror with a radius of curvature (R) of approximately -1.067 cm.

To achieve a 3.6-times magnified virtual image, you will need a concave mirror. Concave mirrors have the ability to create magnified virtual images.

To determine the radius of curvature of the mirror (R), we can use the mirror formula

1/f = 1/v - 1/u

where f is the focal length of the mirror, v is the image distance (negative for virtual images), and u is the object distance.

Given that the magnification (m) is equal to -v/u, and the desired magnification is 3.6, we can write

m = -v/u

3.6 = -v/u

Since the image is virtual, the image distance (v) will be negative. Also, the object distance (u) is given as 4.9 cm.

Plugging in the values into the magnification equation, we get

3.6 = -v/4.9

Solving for v, we find

v = -4.9/3.6

v ≈ -1.3611 cm

Now, substituting the values of v and u into the mirror formula, we have

1/f = 1/(-1.3611) - 1/4.9

Simplifying the equation, we get

1/f ≈ -0.7335 - 0.2041

1/f ≈ -0.9376

Taking the reciprocal of both sides, we find

f ≈ -1.067 cm

The negative sign indicates that the mirror has a concave shape.

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It is possible for a heat engine to receive 500 kJ/s of heat from an 1100-K source and reject 300 kJ/s to a low-temperature sink at 300 K. This scenario is in accordance with the second law of thermodynamics, which states that heat naturally flows from a higher temperature to a lower temperature.

The net rate of change of entropy for this system can be calculated using the equation ΔS = Q_in / T_in - Q_out / T_out, where ΔS is the change in entropy, Q_in is the heat received, Q_out is the heat rejected, T_in is the temperature of the heat source, and T_out is the temperature of the heat sink. The thermal efficiency of a heat engine is given by the formula η = (W_out / Q_in) * 100%, where η is the efficiency, W_out is the work output, and Q_in is the heat input. The maximum efficiency that a heat engine can achieve is given by the Carnot efficiency, which is determined solely by the temperatures of the heat source and heat sink.

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The most liquid asset among the given options is likely to be a traveler's check. Option C is the correct answer.

Among the given options, the most liquid asset is a traveler's check (option C). Liquidity refers to how quickly and easily an asset can be converted into cash without significant loss in value. An automobile (option A) can take time and effort to sell, and its value can depreciate.

A U.S. savings bond (option B) has a fixed maturity date and may require time to redeem. 50 shares of Microsoft stock (option D) can be sold relatively quickly, but the liquidity depends on market conditions and trading volume. A traveler's check (option C) can be easily exchanged for cash at various locations, making it the most liquid asset in this context.

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The question is -

Which of the following assets is the most liquid?

A. an automobile.

B. a u.s. savings bond.

C. a traveler's check.

D. 50 shares of Microsoft stock.

The temperature to which you would have to heat a brass rod for it to be 2.5% longer than it is at 30°C is 218°C (two significant figures).

Explanation: Let's begin with the formula for linear thermal expansion.

ΔL = αLΔT

Here, ΔL is the change in length,α is the coefficient of linear expansion, L is the original length, andΔT is the change in temperature.

The equation can be rearranged as follows:

α = ΔL/LΔT

The coefficient of linear expansion is the change in length per degree Celsius per unit length.

The value of α for brass is given as 1.9 × 10^-5/°C.

So, to solve for the change in temperature required to achieve a 2.5% increase in length,

substitute the values into the formula above:

α = ΔL/L

ΔT1.9 × 10^-5/°C

α= (2.5/100)L/ΔT

The L value can be taken as 1 cm for this problem,

giving:

1.9 × 10^-5/°C = (2.5/100)(1 cm)/ΔT

ΔT = 1 cm/(2.5/100)(1.9 × 10^-5/°C)

ΔT = 218°C  (two significant figures).

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Answer:

diffraction

Explanation:

The behavior of the light incident upon this page best illustrates the phenomenon of diffraction

hope it help:)

The behaviour of such incident light on just this pages adequately exemplifies the phenomena called Diffraction. A further explanation is below.

The broadening out of waveforms when they transit through such an apertures anywhere around obstructions generally referred to as diffraction.

It happens whenever the aperture as well as obstruction seems of the equivalent order of magnitude as that of the transmitted beam's wavelength.

Thus the approach above i.e., option C is correct.

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Answer:

An outside thermometer reads 57°F. What is this temperature in °C? Round your answer to the nearest whole number.

14

49

71

135

answer is A:14

Explanation:

The temperature of the thermometer which reads 57 °F in degree celsius (°C) to the nearest whole number is 14 °C

We can convert from degree celsius (°C) to degree Fahrenheit (°F) with the following equation

°C = 5/9(°F – 32)

°C = 5/9(°F – 32)

°C = 5/9(57 – 32)

°C = 5/9 × 25

°C = 14 °C

Thus, the temperature in degree celsius (°C) of the thermometer is 14 °C

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The statement "foxconn retrofitted the empire state building with led lighting, cutting down on energy consumption by 73 percent." is false as Foxconn did not retrofit the Empire State Building with LED lighting

There is no record or evidence to support the claim that Foxconn, a multinational electronics contract manufacturing company, retrofitted the Empire State Building with LED lighting resulting in a 73 percent reduction in energy consumption. Foxconn is primarily known for its manufacturing operations, particularly in the field of electronics and technology.

The retrofitting of the Empire State Building with LED lighting did occur, but the company responsible for this project was Philips Lighting (now known as Signify). The retrofitting project, completed in 2012, involved replacing the building's traditional lighting fixtures with energy-efficient LED lights, resulting in significant energy savings. However, the reported energy reduction was approximately 38 percent, not 73 percent.

Therefore, the statement claiming that Foxconn retrofitted the Empire State Building with LED lighting, reducing energy consumption by 73 percent, is false.

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Answer:

45

Explanation:

The mass number is 80

Proton number is 35

A-P=n

80-35=45

Explanation:

The potential energy of the roller coaster is due to its position. It can be calculated as :

P = mgh

Where

m is mass, g is acceleration due to gravity and h is height.

The kinetic energy of an object is given by :

[tex]K=\dfrac{1}{2}mv^2[/tex]

Where

v is the speed of the object

At lowest point, the potential energy of the roller coaster is converted to the kinetic energy. So, At the bottom of the slope kinetic energy is at its maximum value and potential energy is at its minimum value. That's why the speed of the cars is at the lowest points in the ride.

We have that for the Question "Which statement explains why the fastest speeds of the car will be at the lowest points in the ride?"

option a explains why the fastest speeds of the car will be at the lowest points in the ride because potential energy decreases with decrease in height. Here the decreased potential energy is converted to the kinetic energy.

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K = (3/2) * 8.314 J/(mol·K) * 413 K. Calculating this expression will give us the average translational kinetic energy for one mole of gas at 413 K.

The average translational kinetic energy, K, for one mole of gas at a given temperature can be calculated using the equation:K = (3/2) * R * T
Where: K is the average translational kinetic energy

R is the ideal gas constant (8.314 J/(mol·K))

T is the temperature in Kelvin

Substituting the given values into the equation:

K = (3/2) * 8.314 J/(mol·K) * 413 K

Calculating this expression will give us the average translational kinetic energy for one mole of gas at 413 K.

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The Cessna 152 is a popular general aviation aircraft. To understand how the required coefficient of lift (CL) and angle of attack (AOA) change with airspeed.

We need to consider the aerodynamic characteristics of the aircraft.

1. Relationship between CL, AOA, and Airspeed:

As airspeed changes, the required CL and AOA for maintaining level flight at a specific weight in the Cessna 152 will also change. Generally, as airspeed increases, the required CL decreases, which means the AOA will also decrease.

At lower airspeeds, such as during takeoff or landing, the Cessna 152 typically operates at higher CL and AOA values. This is because the aircraft needs more lift to overcome its weight and maintain level flight or climb. For example, during takeoff, the required CL and AOA will be relatively high to generate sufficient lift at low speeds.

As the aircraft accelerates and reaches its cruise speed, the required CL and AOA will decrease. This is because the increased airspeed provides more lift and reduces the need for a high CL. In cruise, the Cessna 152 typically operates at lower CL and AOA values compared to takeoff and landing.

To provide specific examples, let's consider the Cessna 152 at a specific weight:

Takeoff: At a lower airspeed during takeoff, the required CL could be around 1.3 to 1.5, and the AOA might be around 10 to 12 degrees.

Cruise: Once the aircraft reaches its cruise speed, the required CL decreases. It could be around 0.6 to 0.8, and the AOA might reduce to around 2 to 4 degrees.

These values are approximate and may vary depending on factors such as weight, aircraft configuration, and atmospheric conditions. It's important to consult the specific aircraft's performance charts or pilot operating handbook for precise values.

CLmax Limit and Associated Speed Regime:

If the required CL exceeds the maximum lift coefficient (CLmax) of the Cessna 152's airfoil, the aircraft will no longer be able to generate sufficient lift at that particular AOA. This condition is commonly associated with the aircraft reaching its critical angle of attack (AOA), beyond which it experiences an aerodynamic stall.

In the Cessna 152, the airfoil typically exhibits a CLmax around 1.4 to 1.6. If the required CL exceeds this value, the aircraft will not be able to maintain level flight or continue to generate enough lift. This condition is often encountered during high-AOA maneuvers, such as during a go-around or during certain phases of stall recovery.

It is important for pilots to be aware of the aircraft's limitations and the associated speed regime where exceeding CLmax may occur. Proper training and understanding of the aircraft's performance characteristics are crucial to ensure safe operation.

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The average and instantaneous velocities in m/s at 8.0 seconds would be 0.5 m/s and  0 m/s respectively, therefore the correct answer is option D.

What is Velocity?

The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.

As given in the problem, this object was moving at a velocity of 1.0 m/s east at the end of 4.0 seconds.

The average velocity of the object = ( 4 - 0 ) / (8 -0)

The instantaneous velocity of the object = 0 m/s

Thus, the average and instantaneous velocities in m/s at 8.0 seconds would be 0.5 m/s and  0 m/s respectively, therefore the correct answer is option D.

Answer:

Explanation:

Answer:

Average = 0.67 m/s east; instantaneous = 0 m/s

Explanation:

took the test

Answer:

The first law, also known as Law of Conservation of Energy, states that energy cannot be created or destroyed in an isolated system.  The second law of thermodynamics states that the entropy of any isolated system always increases.  The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.

Explanation:

Answer: C

Explanation:

The statement "Snell's law gives the change in intensity of a beam of light when it travels from one medium to another" will be evaluated to determine its truthfulness. Option A is correct answer.

Snell's law, also known as the law of refraction, relates the angles of incidence and refraction of a light beam as it passes from one medium to another. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two media.

However, Snell's law does not directly give information about the change in intensity of the light beam. Intensity refers to the amount of power carried by the light per unit area and is related to the square of the amplitude of the electric field. The change in intensity of a light beam when it passes through different media is influenced by factors such as absorption, scattering, and reflection, which are not explicitly described by Snell's law.

Therefore, the statement "Snell's law gives the change in intensity of a beam of light when it travels from one medium to another" is false. Snell's law primarily relates the angles of incidence and refraction, providing information about the direction of the light beam but not directly addressing changes in intensity.

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The complete question is

Snell’s law gives the change in intensity of a beam of light when it travels from one medium to another. group of answer choices true false

A. The higher the index of refraction of a medium

B. The slower light moves within it.

Answer:

20

Explanation:

20 multiplied by 2

hope i hv answered ur question

The pulley must rotate at a speed of approximately 1.99 radians per second for the cable car to make the trip in 12 minutes.

To determine the rotational speed of the pulley, we need to calculate the angular velocity (ω) in radians per second.

Distance traveled by the cable car = 6.8 km

Time taken to make the trip = 12 minutes

First, let's convert the distance to meters:

Distance = 6.8 km = 6,800 meters

Next, let's convert the time to seconds:

Time = 12 minutes = 12 * 60 seconds = 720 seconds

The linear speed (v) of the cable car can be calculated using the formula:

v = distance / time

v = 6,800 meters / 720 seconds

v ≈ 9.44 m/s

The linear speed of the cable car is equal to the circumference of the pulley multiplied by its angular velocity:

v = 2πrω

where r is the radius of the pulley (half of its diameter).

Given the diameter of the pulley is 3.0 m, the radius is:

r = 3.0 m / 2 = 1.5 m

Substituting the values into the equation:

9.44 m/s = 2π(1.5 m)ω

To solve for ω, divide both sides by 2π(1.5 m):

ω = 9.44 m/s / (2π(1.5 m))

ω ≈ 1.99 rad/s

Therefore, the pulley must rotate at a speed of approximately 1.99 radians per second for the cable car to make the trip in 12 minutes.

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Answer:

3m/s is the answer.

Explanation:

f = c/λ

f = frequency

c = speed (m/s)

λ = wavelength

f = c/λ

1.5 = c/2

c = 3m/s

Answer:

[tex]0.025\ \text{m}[/tex]

Yes

Explanation:

[tex]m_8[/tex] = Mass of uranium 238 ion = [tex]3.95\times 10^{-25}\ \text{kg}[/tex]

[tex]m_5[/tex] = Mass of uranium 235 ion = [tex]3.9\times 10^{-25}\ \text{kg}[/tex]

v = Velocity of ions = [tex]3\times 10^5\ \text{m/s}[/tex]

q = Charge of triply charged ions = [tex]3\times 1.6\times 10^{-19}\ \text{C}[/tex]

B = Magnetic field = 0.25 T

The force balance is

[tex]\dfrac{mv^2}{r}=qvB\\\Rightarrow r=\dfrac{mv}{qB}[/tex]

The difference between the radius of the ions are

[tex]\Delta r=(m_8-m_5)\dfrac{v}{qB}\\\Rightarrow \Delta r=\dfrac{(3.95\times 10^{-25}-3.9\times 10^{-25})\times 3\times 10^5}{3\times 1.6\times 10^{-19}\times 0.25}\\\Rightarrow \Delta r=0.0125\ \text{m}[/tex]

Separation is given by

[tex]\Delta d=2\Delta r=2\times 0.0125\\\Rightarrow \Delta d=0.025\ \text{m}[/tex]

The separation between their paths when they hit a target after traversing a semicircle is [tex]0.025\ \text{m}[/tex].

Yes, the distance between the paths is 2.5 cm is a practical separation between as it is easily measurable.

Answer:

[tex]5.2\ \text{m/s}[/tex]

[tex]70^{\circ}[/tex] south of east

Explanation:

[tex]v_a[/tex] = 3 m/s

[tex]\theta_a[/tex] = [tex]20^{\circ}[/tex] north of east

[tex]v_b[/tex] = 6 m/s

[tex]\theta_b[/tex] = [tex]40^{\circ}[/tex] south of east = [tex]360-40=320^{\circ}[/tex] north of east

x and y component of [tex]v_a[/tex]

[tex]v_{ax}=v_a\cos \theta\\\Rightarrow v_{ax}=3\times \cos 20^{\circ}\\\Rightarrow v_{ax}=2.82\ \text{m/s}[/tex]

[tex]v_{ay}=v_a\sin\theta\\\Rightarrow v_{ay}=3\times \sin20^{\circ}\\\Rightarrow v_{ay}=1.03\ \text{m/s}[/tex]

x and y component of [tex]v_b[/tex]

[tex]v_{bx}=v_b\cos \theta\\\Rightarrow v_{bx}=6\times \cos 320^{\circ}\\\Rightarrow v_{bx}=4.6\ \text{m/s}[/tex]

[tex]v_{by}=v_b\sin\theta\\\Rightarrow v_{by}=6\times \sin320^{\circ}\\\Rightarrow v_{by}=-3.86\ \text{m/s}[/tex]

[tex]\Delta v=v_b-v_a\\\Rightarrow \Delta v=(4.6-2.82)\hat{i}+(-3.86-1.03)\hat{j}\\\Rightarrow \Delta v=1.78\hat[i}-4.89\hat{j}[/tex]

Magnitude

[tex]|\Delta v|=\sqrt{(-4.89)^2+1.78^2}\\\Rightarrow \Delta v=5.2\ \text{m/s}[/tex]

Direction

[tex]\theta=\tan{-1}|\dfrac{-4.89}{1.78}|\\\Rightarrow \theta=70^{\circ}[/tex]

The magnitude of the change in velocity vector is [tex]5.2\ \text{m/s}[/tex] and the direction is [tex]70^{\circ}[/tex] south of east.

The change in velocity will be  [tex]\Delta V=5.2\ \frac{m}{s}[/tex] and the direction will be [tex]70^o[/tex] South to east.

Any quantity which is defined by its magnitude and direction both are called as the vector quantities.

Now the data given in the question will be given as:

[tex]V_a[/tex] = 3 m/s

[tex]\theta[/tex] = [tex]20^o[/tex] north of east

[tex]V_b[/tex] = 6 m/s

[tex]\theta[/tex] =  [tex]40^o[/tex]south of east =  360-40=320 north of east

Now we will find the x and y component of [tex]V_a[/tex]

[tex]V_{ax}=V_acos\theta[/tex]

[tex]V_{ax}=3\times Cos20[/tex]

[tex]V_{ax}=2.82\ \frac{m}{s}[/tex]

[tex]V_{ay}=V_aSin\theta[/tex]

[tex]V_{ay}=3\times Sin20[/tex]

[tex]V_{ay}=1.03\ \frac{m}{s}[/tex]

Now we will find the x and y component of [tex]V_b[/tex]

[tex]V_{bx}=V_bcos\theta[/tex]

[tex]V_{bx}=6\times cos\320[/tex]

[tex]V_{bx}=4.6\ \frac{m}{s}[/tex]

[tex]V_{by}=V_bSin\theta[/tex]

[tex]V_{by}=6\times Sin320[/tex]

[tex]V_{by}=-3.86\ \frac{m}{s}[/tex]

Now change in velocity will be

[tex]\Delta V=V_b-V_a[/tex]

[tex]\Delta V=(4.6-2.82)i+(-3.86-1.03)j[/tex]

[tex]\Delta V=1.78i-4.89j[/tex]

The magnitude can be find out as follows:

[tex]\Delta V=\sqrt{(-4.89^2+(1.78^2)}[/tex]

[tex]\Delta V=5.2\ \frac{m}{s}[/tex]

The direction of the vector will be

[tex]\theta= tan^{-1}(\dfrac{-4.89}{1.78})[/tex]

[tex]\theta=70^o[/tex]

Thus the change in velocity will be  [tex]\Delta V=5.2\ \frac{m}{s}[/tex] and the direction will be [tex]70^o[/tex] South to east.

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