Which statement is true about vectors?
a. All quantities in physics are not vectors.
b. A vector may have either magnitude or direction.
c. The vector’s length should be proportional to its magnitude.
d. Two vectors can be added only if they have the same direction.

(a) The plane must fly at an angle of N 35.5° E to immediately approach the lake.

(b) The velocity of the plane is 245.6 km/h.

(c) The time taken is 1.02 hours.

Lake displacement from the starting position, D = 250 km N 30° E

As the x-axis, let's choose the line connecting the plane's beginning point with the lake, which is located in the direction N 30° E.

D = 250 ^i km

The plane's airspeed,

v(p) = 210 km/h

From the east comes the wind. Therefore, using the coordinate system described above, the wind speed,

v(w) = 40 [ cos ( − 30° ) ^i + sin ( − 30°) ] km/h

v(w) ≈ ( 36.64 ^i − 20 ^j ) km/h

(a) To eliminate the perpendicular component of the wind velocity, move the plane in the direction θ with respect to the x-axis.

v(p) = 210 ( cos(θ) ^i + sin(θ) ^j ) km/h

In order for the y-component of the plane velocity to cancel out the y-component of the wind velocity, the correct angle must be calculated.

Therefore,

210 sin(θ) km/h = 20 km/h

sin(θ) = 20 / 210

θ ≈ 5.5°

Therefore, the aircraft should fly 5.5 degrees off of the x-axis. This means that the plane must fly at an angle of N 35.5° E to immediately approach the lake.

(b) The velocity relative to the ground is:

v = v(w) + v(p)

v = 210 ( cos 5.5° ^i + sin 5.5° ^j ) km/h + ( 36.64 ^i − 20 ^j ) km/h

v ≈ ( 209 ^i + 20 ^j ) km/h + ( 36.64 ^i − 20 ^j ) km/h

v = 245.6 ^i km/h

The plane is moving at a speed of 245.6 km/h relative to the ground.

(c) From the starting point, the time taken to reach the lake is:

time = distance/ speed

T = 250 km / 245.6 km/h

T ≈ 1.02 h

Therefore, from the starting position, it will take around an hour to get to the lake.

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The correct answer is S = 28.802 m.

Unless driven to change its condition by an external force, a body stays in its state of rest or uniform motion along a straight line. According to the law, a force is a factor that has the power to alter an object's status. Newton uses the inertia of rest, the inertia of motion, and the inertia of direction to explain his first law of motion.

From Newtons 1st equation of motion

V = u+at

3.06 = 0+0.8[tex]t_1[/tex]

[tex]t_1[/tex] = 3.825 s

Submarine travels [tex]t_2[/tex]= 5s with const velocity

and then again [tex]t_2[/tex]=5s for slowing to strip during slow,

0 = 3.06 - a × 5

a = 0.612 m/[tex]s^2[/tex]

Total time =[tex]t_1 + t_2 + t_3[/tex]

T = 13.825 s

Now [tex]v^2= u^2[/tex]+2as

[tex]S_1[/tex]= (3.06[tex])^2[/tex]/2×0.8

[tex]S_1[/tex] = 5.852 m

[tex]S_2[/tex] = Ut

[tex]S_2[/tex] = 3.06 × 5

[tex]S_2[/tex] = 15.3 m

[tex]S_3[/tex] = 0 - (3.06[tex]) ^2[/tex]/-2 × 0.612

[tex]S_3[/tex] = 7.65 m

Total displacement

[tex]S = S_1+S_2+S_3[/tex]

S = 28.802 m

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The time taken by cheetah to catch its prey is  9.71 s.

Speed is the defined as the distance covered per unit time by a moving body or object.

The speed of the gazelle = 79.9 km/h = 22.2 m/s

speed of the cheetah = 108 km/h = 30 m/s

Let distance covered by gazelle = d

distance covered bet cheetah = d + 75.8

The time taken is same for both = t

time = distance/speed

time taken by cheetah = d + 75.8/30

time taken by gazelle = d/22.2

equating both times: d + 75.8/30 = d/22.2

30 d - 22.2 d = 1682.76

d = 215.7 m

Therefore, time taken by cheetah = (215.7 + 75.8)/30

t = 9.71 s

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Explanation:

i hope this is the right way to solve it

The displacement between 5 s and 20 s in the position-time grap is +40 m

Displacement is defined as the distance travelled in a specific direction. It can be obtained mathematically as:

Displacement = Displacement 2 - Displcemrnt 1

With the above information, we can obtain the displacement. Details below.

From the question given above, we can obtain the displacement as follow:

Displacement = Displacement 2 - Displcemrnt 1

Displacement = 50 - 10

Displacement = +40 m

Thus, the displacement is +40m

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Missing part:

See attached photo

The gas that has the largest proportional increase in mass when moving from the upper troposphere to the surface is water vapor.

As we move away from the earth surface, we encounter a region of gases. This thin layer of gases that overlay the surface of the earth is what we call the atmosphere. There are many gases that are part of the atmosphere.

As we move away form the atmosphere, we encounter another region that lies shortly above the atmosphere called the troposphere. There is a lot of water in the troposphere because it is quite close to the earth surface.

Hence, the gas that has the largest proportional increase in mass when moving from the upper troposphere to the surface is water vapor.

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A mass of 10 kg is dropped from height of 20 m. ignoring air resistance, maximum speed it achieves is 20m/s.

Here on Earth, we tend to take the air resistance (aka. “drag”) for granted. We just assume that when we throw a ball, launch an aircraft, deorbit a spacecraft, or fire a bullet from a gun, that act of it traveling through our atmosphere will naturally slow it down. But what is reason for this? Just how is air able to slow object down, whether it is in free-fall or in flight?

Because of our reliance on air travel, our enthusiasm for the space exploration, and our love of sports and making things airborne (including ourselves), understanding air resistance is key to understanding physics, and integral part of many scientific disciplines. As part of subdiscipline known as fluid dynamics, it applies to the fields of aerodynamics, hydrodynamics, astrophysics, and nuclear physics (to name a few).

By definition, the air resistance describes the forces that are in opposition to the relative motion of an object as it passes through the air. These drag forces act opposite to oncoming flow velocity, thus slowing the object down. Unlike other resistance the forces, drag depends directly on velocity, since it is the component of the net aerodynamic force acting opposite to the direction of the movement.

so,

PE = mgh = 10 kg x 10 m/s^2 x 20 m = 2000 J

KE = 1/2 mv^2

2000 J = 1/2 x 10 kg x v^2

4000 J = 10 v^2

400 = v^2

20 = v

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The field to rotate this dipole from an orientation of 36.0 does a lot of work. In order to find out how much work is done, we need to consider the rotational energy of the dipole. The rotational energy is given by:

E = 1/2 * I * omega^2

where I is the moment of inertia of the dipole and omega is the angular velocity. From the given information, we can calculate the rotational energy to be:

E = 1/2 * I * (36.0 * 2 * pi / 360)^2

= 1/2 * I * 4 * pi^2

= 2 * I * pi^2

Thus, the work done by the field is:

W = 2 * I * pi^2 * 36.0

= 72 * I * pi^2

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1) The body moved from 0 cm to 4 cm at a constant speed of 1 cm/s.

2) The object moved at a constant speed of 3 cm/s from 0 cm to 3cm

3) Two objects are speeding up and one object is slowing down.

4) The object moved from 4s to 8s at a constant speed of 4 cm/s

5) The horizontal line appears at 5 m/s is the second graph.

We know that acceleration has to do with the change of of velocity of an object with time.

1) We can see that the position changes by equal amounts in equal time intervals thus the body moved from 0 cm to 4 cm at a constant speed of 1 cm/s.

2) Looking at the shape of the second graph we can see that the object moved at a constant speed of 3 cm/s from 0 cm to 3cm

3) From the images of the ticker tapes, we can see that two objects are speeding up and one object is slowing down.

4) From the fourth graph, we can see that the object moved from 4s to 8s at a constant speed of 4 cm/s

5) The graph in which the horizontal line appears at 5 m/s is the second graph.

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With the use of second equation of motion formula, its position at time 3.7 s is 16.43 meters

A position is a point where an object can be located. The length between two positions is known as distance.

Given that a ball starts from rest at the initial position xi = 0. The ball has a constant acceleration of 2.4m/s², to know its position time 3.7 s, we will use the formula

X2 - X1 = ut + 1/2 × a × t²

Where

Substitute all the parameters into the formula

X2 - 0 = 0 + 1/2 × 2.4 × 3.7²

X2 = 1.2 × 13.69

X2 = 16.43 m

Therefore, its position at time 3.7 s is 16.43 meters

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Answer:

V1 = 700 cos 69.8 i + 700 sin 69.8 j           vector components of V1

V1 = 241.7 i + 656.9 j          in miles/hour

V2 = 620 cos 107  i + 620 sin 107 j

V2 = -181.3 i + 592.9 j

V = V1 - V2 = 423 i + 64 j        rate of planes separation

1.9 V = 803.7 i + 121.6 j     miles   separation of planes after 1.9 hr

D = (803.7^2 + 121.6^2)^1/2 = 812.8 miles

The absolute value of the price elasticity of demand is 0.46.

What is price elasticity of demand?

The price elasticity of demand is used to determine the quantity sought after for a good. When prices rise, demand declines for almost all products, but some products are more negatively impacted than others. When a price increases by 1% while all other factors remain constant, the price elasticity provides the percentage change in quantity required. A 1% increase in price results in a 2% decrease in demand when the elasticity is negative two. The effects of changes in other parameters on the needed quantity are evaluated by other elasticities (e.g. the income elasticity of demand for consumer income changes).

What does the microeconomic midpoint technique entail?

With the midpoint formula, percentage changes are calculated by dividing the change by the average, or halfway point, between the starting and final values. As a result, the outcome is the same regardless of the direction of the change.

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Question:

Price Quantity

250 0

200 30

150 70

100 110

50 150

0 190

Using the midpoint method, if the price falls from $100 to $50, the absolute value of the price elasticity of demand is

a. 0.31.

b. 0.46.

c. 1.25.

d. 2.17

Create a plate with three points of reference. On the two side points put the two compounds separately and in the middle one combine both compounds.

The Rf value of a substance is used to identify the properties of that compound. The Rf value of polar compounds is lower, while the Rf value of non-polar compounds is higher. Three lanes are the most prevalent method for assessing too close spots. Compound A is in lane 1. Compound B is in lane 3. Both spots are in lane 2. This is known as a co-spot. If the co-spot exhibits a 'snowman' effect whenever the TLC is run, it indicates that perhaps the spots are, in a real sense, different compounds which are extremely close together. You could also try changing the solvent system, yet co-spot always comes first.

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Answer:

1.69 km away from the finish line.

Explanation:

velocity =distance/time

time= distance/velocity so 8km/14.3km per hour equal to 80/143 hr or 0.559 hrs for second runner to finish race

therefore 0.559 multiply by velocity to give distance of first runner when second runner finish race

0.559 times by 11.3= 6.32 km (3 significant figures)

8 km - 6.32km

= 1.69 km away from the finish line.

Average speed = 3.6km/h

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Calculating the ratio of the body's total distance traveled to the time needed to complete that distance yields the average speed formula. As stated in the average speed equation:

S average =  Total Distance traveled/Total Time taken

A scalar value represents the average speed. The change in position or displacement (x) divided by the time intervals (t) during which the displacement happens is the definition of average velocity. The average velocity is measured in meters per second or M/s.

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To express of an electron we have to figure out the relationship between momentum and wavelength:

λ= [tex]\frac{h}{p}[/tex]  =[tex]\frac{h}{mv}[/tex]

So, velocity of an electron will be:

v= me/λ[tex]e[/tex]h

​h= Planck's constant

[tex]m_{e}[/tex] = mass of the electron

Now we will see what is its value:

V= h/mcλ

[tex]\frac{6.626 .10^{-34}J.s}{(9.109.10^{-31}kg).(100.10^{-12m)} }\\ 7.27.10^{6} m.s^{-1}[/tex]

​Now, to express accelerating potential energy difference we will use kinetic energy and charge of electron

Kinetic energy: [tex]E_{K} =e_{E}[/tex]

But kinetic energy in terms of velocity is

:[tex]\frac{(9.109.10^{-31}kg).(7.27.10^{6}ms^{-1})^{2} }{2.(1.602.10^{-19} C)} \\=150.210^{-31} .10^{-31} .10^{12}.10^{19}V \\ = 1.502.10^{2}V[/tex]

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The rate of water expressed in ft³/s is: 0.1423 ft³/s

To solve this problem, we have to do the conversion of units with the given information.

Information about the problem:

By Converting the units from (gal/min) to (ft³/s), we get:

rate of water = 63.9 gal/min * 1 ft³/7.481 gal * 1 min/60 s

rate of water =0.1423 ft³/s

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

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It will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.

The stopping distance of a body moving with constant acceleration can be calculated by using the following equation,

v^2 - u^2 = 2as

As the body has stopped, v will be zero.

v^2 - u^2 = 2as

The stopping distance comes out to be

s = u^2/2a

As the stopping distance is proportional to the square of the initial velocity of the body, the mass of the body does not have any effect on the stopping distance.

So, both a car and a tractor-trailer will have the same stopping distance when moving at the same speed.

Therefore, it will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.

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It will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.

The stopping distance of a body moving with constant acceleration can be calculated by using the following equation,

v^2 - u^2 = 2as

As the body has stopped, v will be zero.

v^2 - u^2 = 2as

The stopping distance comes out to be

s = u^2/2a

As the stopping distance is proportional to the square of the initial velocity of the body, the mass of the body does not have any effect on the stopping distance.

So, both a car and a tractor-trailer will have the same stopping distance when moving at the same speed.

Therefore, it will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.

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By Avogadro's number, the mass is 1.12 x 10¯²⁰ gram.

We need to know about Avogadro's number to solve this problem. Avogadro's number is the number that explains how many atoms are in one mol. The Avogadro's number is

Na =  6,02 × 10²³ atoms / mol

From the question above, we know that

N = 172 atoms

Ar = 39.1

By using Avogadro's number, we can calculate the amount of potassium

N = Na . n

172 = 6,02 × 10²³ . n

n = 2.86 x 10¯²² mol

Find the mass

n = gr / Ar

2.86 x 10¯²² = gr / 39.1

gr = 1.12 x 10¯²⁰ gram

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Answer: 5. 9000 meters

6. 0.12626 miles

7. 26.78 meters

8. 1 mile per minute

9. 468 km per hour

Explanation:

5. 1000 m=1 km

9 km * 1000 m/1 km=

9 * 1000/1 = 9000 meters

6. 63360 inches = 1 mile

8000 inches * 1 mile/63360 inches=

8000/63360=0.12626 miles

7. 100 cm=1 m

2678 cm * 1 m/100 cm=

2678 * 1/100=

2678/100=26.78 meters

8. 60 minutes=1 hour

60 mph * 1 hour/60 minutes=

60 * 1/60=1 mile per minute

9. 1000 m=1 km

1 hour=60 minutes

1 minute=60 seconds

60 seconds * 60 minutes/1 hour=

60 * 60/1=3600 seconds

130 meters * 3600 seconds/1 second=

130 * 3600/1=468000 meters per hour

468000 m* 1 km/1000 m=

468000 * 1/1000=468 km per hour

in that scenario, the signaling rate is exclusively constrained by the channel bandwidth according to Nyquist's analysis of the theoretical capacity of a noiseless channel.

• What signaling rate can be accomplished over a channel with a certain bandwidth, a given signal power, and in the presence of noise was addressed by Shannon.

• Channel without errors The temperature of a material is defined as the average kinetic energy of its atoms or molecules, plus any other energy that can be transferred. In theory, the lower limit of temperature would be when all particles have zero energy

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The change in the internal energy of the system in kilojoules is 142 kJ.

The internal energy of a system is defined as the sum of work done by a system or work done on a system and heat released by the system or heat gained by a system. Internal energy is represented by the symbol U. It is presented in units of kilojoules.

Work done by the system is W.

W = (-37) kJ

The heat released by the system is U.

U = (-105) kJ

The change in the internal energy of the system in kJ is,

Change in internal energy = Heat + Work done

∆ U = Q + W

∆ U = (-105) + (-37)

∆ U = 142 kJ

Therefore, the change in the internal energy of the system in kilojoules is 142 kJ.

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The object will fall a distance during its final second in the air of: 81.967 m

The free fall formulas and the procedures we will use are:

Where:

Information of the problem:

Applying the time formula we get:

t = √[ (2*h) / g]

t = √[ (2* 127 m) / 9.8 m/s²]

t = √[ 254 m / 9.8 m/s²]

t = √[ 25.918 s²]

t = 5.090 s

Calculating time traveled before the final second and we have:

t(final second) = t - 1 s

t(final second) = 5.090 s - 1 s

t(final second) = 4.090 s

Applying the height formula we get:

h = (g * t²)/2

h(final second) = (9.8 m/s² * (4.090 s)²)/2

h(final second)  = (9.8 m/s² * 16.7281 s²)/2

h(final second) = 163.935 m/2

h(final second) = 81.967 m

It is when the object or mobile falls from a height (h) with a positive acceleration equal to the gravity, describing a vertical rectilinear travel.

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The block with the greatest density = Block A

The block with the lowest density = Block B

The density of an object is the ratio of mass to volume of the object.

density = mass/volume

The given density of the object;

Thus, we can conclude the following based on the density of the objects;

The block with the greatest density = Block A

The block with the lowest density = Block B

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Answer:

B.rate of convection

Explanation:

Answer:

1. Atoms are the smallest units of matter.

2. Atoms are composed of protons, electrons, and neutrons.

3. The protons and neutrons are located in the nucleus, and the electrons orbit around the nucleus.

4. The properties of atoms are determined by the number of protons in the nucleus.

Explanation:

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6.21 ×10⁻¹⁹ J  energy of a photon of this wavelength

374028.3 J the energy of a mole of these photons

1) E =hc/λ

=  (6.626×10⁻³⁴×3×10⁸)/(320*10⁹)

= 6.21×10⁻¹⁹ J

2) Of 1 mole E = Avogadro no.*Energy of one photon

= 6.21×10⁻¹⁹×6.023×10²³

= 374028.3 J

3) n×(6.21×10⁻¹⁹) = (10⁻³)

Thus n = 1.61×10¹⁵

How does one find the energy of a photon?

The energy of a photon are often calculated in two ways: If the photon's frequency f is known, we will use the formula E = h f . Planck proposed this equation, which is why it's known as Planck's equation. If the photon's wavelength is understood , the photon's energy are often calculated using the formula E = h c λ

What is the charge of photon?

A photon may be a tiny particle that comprises waves of electromagnetic radiation. As shown by Maxwell, photons are just electric fields traveling through space. Photons haven't any charge, no resting mass, and travel at the speed of sunshine

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Starting from rest, a 2-kg body acquires a speed of 8 m/s in 2 seconds. the net force acting on the body is: 8 N

To solve this exercise the formula for net force and the formula for uniformly varied rectilinear motion (UVRM) to be applied are:

Where:

Information about the problem:

Applying the formula for UVRM we can calculate the acceleration of the runner:

a = (vf - vi) /t

a = (8 m/s - 0 m/s) / 2s

a = 8 m/s / 2s

a = 4 m/s²

With the acceleration we can apply the net force formula and get:

F = m * a

F = 2 kg * 4 m/s²

F = 8 N

It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.

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