The distance travelled due east during the trip is 875.831 meters.
The distance due west is 6.44 km (6440m) and the velocity due west is 2.6m/s. The velocity due east is 0.465m/s.
We know,
Average velocity = Total displacement/Total time
It is given that, the total average velocity is 0.465m/s.
If distance in west is W and the distance in east is E, then the displacement D is,
D = √((6440)²+(E)²)
The time T₁ in west,
T₁ = 6440/2.6 seconds
Time time T₂ in east,
T₂ = E/0.465
The total time T is,
T = T₁ + T₂
T = 6440/2.6 + E/0.465
So, putting all the values now,
Average velocity = D/T
1.37 = √((6440)²+(E)²)/(6440/2.6 + E/0.465)
On solving it further,
We get,
E = 875.831 meters.
So, the distance in east is 875.831 meters.
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an interference pattern is produced by four parallel and equally spaced narrow slits. by drawing appropriate phasor diagrams, explain why there is an interference minimum when the phase difference from adjacent slits is:
The minimum interference when the phase difference from adjacent slits is ( A1 -A2)².
The amplitude of a periodic variable is the degree of its change in a single duration. The amplitude of a non-periodic signal is its important as compared with a reference cost. there are various definitions of amplitude, which are all features of the magnitude of the variations between the variable's excessive values.
Let A1 be the amplitude of the 1st wave and A2 be the amplitude of the 2nd wave.
Let the resultant amplitude be A.
the formula of interference, we get,
A= (A1)²+(A2)²+ 2×A₁× A₂ (cos theta)
When theta = 180 degrees = π radian, cos π= -1
Putting the value of cos theta in the equation we get,
A= (A1)² +(A2)² - 2×A1×A2
A= ( A1 -A2)²
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A baseball has a mass of 2.5 kilograms. If the acceleration due to gravity is 9.8 m/s2 , what is the weight of the baseball in newtons?
A. 20.0 N
B. 3.9 N
C. 10.5 N
D. 24.5 N
Answer: D. 24.5 N
Explanation:
Fgrav = mg
Fgrav = 2.5(9.8)
Fgrav = 24.5 N
b. Which station broadcasts waves with a shorter wavelength
Answer:
blue and purple light
Explanation:
Light waves have very, very short wavelengths. Red light waves have wavelengths around 700 nanometers (nm), while blue and purple light have even shorter waves with wavelengths around 400 or 500 nm.
what is the conversion efficiency (power coefficient) from power in the wind to electrical power output for a modern highly engineered horizontal axis high-tip-speed two blade wind turbine? group of answer choices
The conversion efficiency from the power in the wind to electrical power output for a modern highly engineered two blade wind turbine is 35 % to 45%.
What is power coefficient and how the conversion efficiency from power in wind to turbine is so?Power coefficient is similarity in relation to power just combining the flow coefficient and head coefficient.Power coefficient is denoted by Cp and whose equation is like Cp= f( Vwind) where V is the velocity of the wind.Here in the question is asked the conversion efficiency from power in wind to the power in wind turbine.So the conversion efficiency from the power in the wind to the electrical power output for a modern highly engineered two blade wind turbine is 35% to 45%.To know more about power coefficient visit:
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What is your total displacement if you walk 30m East and 50m North?
The total displacement would be 110m.
The total distance is 50 m + 30 m + 30 m = 110 m. The displacement is the shortest route from the starting point. It is solved using vectors.
What is Displacement?
Displacement is a vector quantity which depends on the direction of motion but distance is a scalar quantity which just sums up all the given quantity values. The displacement is simply the difference between the locations of the two markers and is unrelated to the route used to get there. It is a vector quantity that has a direction and magnitude.
Hence, the total displacement if you walk 30m East and 50m North would be 110m.
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Answer:
58.31 meters northeast
Explanation:
The displacement can be modeled into the vector equation of [tex]\displaystyle{\vec s = 30\hat x + 50\hat y}[/tex]. We can find the magnitude of displacement by applying Pythagoras Theorem. Suppose we have a two-dimensional vector equation [tex]\displaystyle{\vec v = a\hat x + b\hat y}[/tex] then the magnitude of vector is [tex]\displaystyle{|\vec v\, | = \sqrt{a^2+b^2}}[/tex].
Therefore, the magnitude of displacement is:
[tex]\displaystyle{|\vec s\, | = \sqrt{30^2+50^2}}\\\\\displaystyle{=\sqrt{900+2500}}\\\\\displaystyle{=\sqrt{3400}}\\\\\displaystyle{\approx 58.31 \ \sf m}[/tex]
Since 30 meters east and 50 meters north form northeast direction then the displacement is 58.31 meters northeast.
the magnetic field of a long, straight wire has a value b0 at a distance of r0 when the current is i0. at a distance of 3.00 r0. what current is necessary to produce a field having the same strength b0 at this position?
The magnetic field of a long straight wire has a board b0 at a distance r0 when the cutting edge is i0. at a distance of 3.00 r0: B'=2B0.
A magnetic field is a vector domain that describes the magnetic effect on moving electricity costs, currents, and magnetic materials. Transfer fees in magnetic fields are under pressure perpendicular to personal speed and magnetic fields.
The magnetic field is the place around the magnet where the effect of the magnetism is felt. We use magnetic fields as tools to explain how magnetic forces are directed into circular space and are essentially magnetic. This force attracts or repels magnets to each other. Examples of magnetic forces include compasses, motors, magnets that keep things in refrigerators, learning tracks, and new roller coasters. All the carrying charges create a magnetic field, and the charges flowing through that area enjoy the force.
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The potential energy of a roller coaster is 50 joules. The kinetic energy of the same coaster is 50 joules. What is the mechanical energy of the coaster?.
Mechanical energy of the coaster is 100 joules.
We need to know about mechanical energy to solve this problem. Mechanical energy is the sum of the potential energy and kinetic energy of an object. It can be written as
E = KE + PE
where E is mechanical energy, PE is potential energy and KE is kinetic energy.
From the question above, the given parameters are
KE = 50 J
PE = 50 J
By substituting the given parameters, we can calculate mechanical energy
E = KE + PE
E = 50 + 50
E = 100 J
The total energy is 100 joules
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in general, what is true about the frequency at which an object vibrates? multiple choice question. the slower the vibrations, the softer the sound the slower the vibrations, the higher the pitch the faster the vibrations, the louder the sound produced the faster the vibrations, the higher the pitch
The statement that is true concerning the frequency include the following: slower the vibrations, the softer the sound, the faster the vibrations, the louder the sound produced and the faster the vibrations, the higher the pitch. That is option A,C and D.
What is sound?Sound is defined as the type of wave that is being created when disturbance causes vibration through a medium such as water, air or solid medium.
The properties of a sound wave include the following:
Frequency,Pitch,Wavelength andAmplitude.The frequency of the sound wave is affects other properties which is the number of sound waves a sound produces per second.
A low frequency would lead to low sound and pitch production while a high frequency would lead to a high sound and pitch production.
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A constant force is used to punch a box along the floor a distance of 3 meters by applying 300j what is the magnitude of force?
The magnitude of the force is equal to 100 newtons.
How do you prove that?It's easy! You just need to divide the work by the displacement:
300 = F · 3
300 = 3F
300/3 = 3F/3
100 = F
F = 100
Here, F is the magnitude of force. The standard unit for force is newton (N). Recall that in physics, work is mathematically defined as W = F · x where W is work, F is force, and x is displacement. The standard unit for work is joule (J) and the standard unit for displacement is meter (m).
You are given that the work applied is equal to 300 joules and the displacement is equal to 3 meters. The force used to punch a box along the floor would then be 100 newtons.
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if the velocity of a pitched ball has a magnitude of 43.5 m/sm/s and the batted ball's velocity is 56.0 m/sm/s in the opposite direction, find the magnitude of the change in momentum of the ball and of the impulse applied to it by the bat.
1.82 kgm/s and 1.82 s^-1 is momentum of the ball and of the impulse respectively applied to it by the bat.
ball mass, m = 0.145 kg
velocity of the pitched ball, v₁ = 43.5 m/s
velocity of the batted ball, v₂ = 56.0 m/s
change in the momentum is
[tex]\Delta P=mv_1-mv_2[/tex]
ΔP=6.30-8.12
ΔP=-1.82 kgm/s
The ball's change in momentum is equal to the impulse it experiences.
[tex]J=\Delta P= 1.82/s[/tex]
A moving particle's change in dynamical state can be estimated using the physical quantity known as impulse. It is the change in momentum that a body experiences when it is briefly impacted by a force. It is a vector quantity, and the letter J is used to denote it.
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a wire with diameter 2.0 mm and length of 10 m is made of an unknown material. the wire has a resistance of 4.2 ohm. calculate the resistance of a wire with a 1.6 mm diameter and 20 m length made of the same material
The resistance of a wire with a 1.6 mm diameter and 20 m length made of the same material is 3.14×10⁻⁷Ω−m.
What does "resistance" mean?Electrical resistance of a conductor with a unit cross-sectional area and unit length is called resistivity. Resistivity is a distinctive attribute of any material that may be used to compare different materials based on how well they conduct electric currents. Low conductivity is indicated by high resistance.
Given,
l= 10m= 1000mm
d= 2mm
∴radius(r)= 20.2 =0.1mm
R=10Ω
To find,
Resistivity(ρ)
ρ=R /l A
where,
R= Resistance
l= Length of wire
A= Cross sectional area of wire
Cross sectional area of cylinder (A)=Πr²
A= π×(0.1)²
A=0.0314mm²
ρ=10(10000.0341)
ρ=0.000314Ω−mm
ρ≃3.14×10⁻⁷Ω−m
So, the resistivity of the material is equal to 3.14×10⁻⁷Ω−m.
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A soccer ball is kicked upward from a height of 6 ft with an initial velocity of 96 ft/s. How high will it go? Use -32 ft/s? forthe acceleration caused by gravity. Ignore air resistance.
Given,
The initial height of the soccer ball, h₁=6 ft
The initial velocity of the ball, u=96 ft/s
The acceleration due to gravity, g=-32 ft/s
When the ball reaches the maximum height, its velocity will reduce to zero.
Thus the velocity of the ball when it is at its maximum height is v=0 ft/s
From the equation of motion,
[tex]v^2-u^2=2gh_2[/tex]Where h₂ is the total height covered by the ball from its initial height to reach its maximum height.
On substituting the known values,
[tex]\begin{gathered} 0-96^2=2\times-32\times h_2 \\ \Rightarrow h_2=\frac{-96^2}{2\times-32} \\ =144\text{ ft} \end{gathered}[/tex]Thus the maximum height reached by the ball is,
[tex]\begin{gathered} H=h_1+h_2 \\ =6+144 \\ =150\text{ ft} \end{gathered}[/tex]Thus the maximum height reached by the ball is 150 ft.
A radio announcer's voice is transmitted via radio waves a distance of 469.06 km. How much time, in microseconds, will it take to transmit the wave over this distance?
Assuming the wave is being transmitted on the vacuum, we know that the velocity of an electromagnetic wave on vacuum is c. We can use the following relation:
[tex]v=\frac{\lambda}{T}\Rightarrow T=\frac{\lambda}{c}=\frac{469.06*10^3}{3*10^8}=1.5635ms=1563.5\mu s[/tex]Thus, our final answer is T=1563.5us
OPEN ENDED QUESTION
The skater eventually comes to a stop.
What has happened to all of the skater's
original potential energy?( this is on the Ed puzzle skate park please help I’m about to cry
Answer:
The maximum amount of kinetic energy the skateboarder can have is entirely dependent on the amount of potential energy of the system.
Explanation:
As the skateboarder moves, her potential energy is converted to kinetic energy (KE), or the energy of motion as her position changes along the track and the velocity changes.
Answer:
Explanation:
Kinetic energy turned into internal energy.
Potential energy has not changed.
The element lanthanum has an isotope with an atomic mass of 138. 9 amu and an abundance of 99. 91%. A second isotope has an atomic mass of 137. 9 amu and an abundance of 0. 9%. What is the average atomic mass of lanthanum?.
Considering the definition of atomic mass, isotopes and atomic mass of an element, the average atomic mass of lanthanum is 151.186 amu.
Definition of atomic massThe atomic mass is obtained by adding the number of protons and neutrons in a given nucleus of a chemical element.
Definition of isotopeThe same chemical element can be formed by different atoms, that is, their atomic numbers are the same, but the number of neutrons is different, thus generating the isotopes of the element.
Definition of atomic massThe atomic masses of chemical elements are usually calculated as the weighted average of the masses of the different isotopes of each element, taking into account the relative abundance of each of them.
Atomic mass of the element in this caseIn this case, you know:
The first isotope has an atomic mass of 138.9 amu and an abundance of 99.91%.The second isotope has an atomic mass of 137.9 amu and an abundance of 0.09%.The average mass of lanthanum can be calculated as:
average mass of lanthanum= 138.9 amu×0.9991 + 137.9 amu×0.09
average mass of lanthanum= 151.186 amu
Finally, the average atomic mass of the element in this case is 151.186 amu.
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air is moving at a velocity of 8 m/s through a hoop with cross sectional area of 100.0 m2. if the density of the air is 1.2 kg/m3, what mass flow rate of air is moving through the hoop (in kg/s)?
In consideration of Henry's law the molar mass of organic compound is 0.24 grams.
What is molar mass?
The mass of a sample of a chemical compound divided by the quantity, or number of moles in the sample, measured in moles, is known as the molar mass of that compound. What is the mass of water in grammes and how much Equis paper with a 12.5% sodium chloride content weighs at 55 degrees Celsius, according to Sol-One of three? His issue informs us that pure water has a specific gravity of 118 torr at 55 degrees Celsius. Therefore, the first task at hand is to determine the mole fraction of, I suppose, the thermal fractions of both water and sodium chloride.
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On average, there is enough wind in the UK each year to supply all of the UK's electricity needs.
Explain why the UK may still need power stations that use fuel to generate electricity
Explanation:
Unplanned maintenance at nuclear plants and lower than average wind speeds mean the country is currently relying on gas-powered stations to generate about half its electricity.
Neptune has a mass that is about 17 times the mass of earth. the distance between the sun and neptune is about 30.1 times the distance between the sun and earth. if the gravitational force between the sun and earth is 3.5 x 1028 n, which is closest to the force between neptune and the sun? 6 x n 6 x n 6 x n 6 x n
Answer: 6 x 10^26 N
Explanation:
a satellite is in a circular orbit around an unknown planet. the satellite has a speed of 1.31 x 104 m/s, and the radius of the orbit is 3.88 x 106 m. a second satellite also has a circular orbit around this same planet. the orbit of this second satellite has a radius of 9.96 x 106 m. what is the orbital speed of the second satellite?
The orbital speed of the second satellite with same centripetal force is 2.1 x 10⁴ m/s.
We need to know about centripetal force to solve this problem. The centripetal force is a force caused by moving objects in a circular motion. The magnitude of the centripetal force depends on tangential speed, mass and radius. It can be written as
Fc = m . v² / r
where Fc is the centripetal force, m is mass, v is tangential speed and r is the radius.
From the question above, we know that
Fc 1 = Fc 2 = Fc
m1 = m2 = m
v1 = 1.31 x 10⁴ m/s
r1 = 3.88 x 10⁶ m
r2 = 9.96 x 10⁶ m
Hence, the ratio of centripetal force is
Fc2 / Fc1 = (m2 . v2² / r2) / (m1 . v1² / r1)
v1² / r1 = v2² / r2
(1.31 x 10⁴)² / 3.88 x 10⁶ = v2² / 9.96 x 10⁶
v2² = 4.41 x 10⁸
v2 = 2.1 x 10⁴ m/s
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a child moves on x axis at a starting point 10cm it moves till it reaches point 70cm then it goes back to 5.
What's the displacement?
What's the distance?
The displacement on x-axis is 75 cm and the distance that moved by the child is 80 cm
The term displacement refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. And distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.We are given that,
Starting point of child = d₁ = 10cm
Reaching point of the child = d₂ = 70cm
Move back = 5cm
Therefore, total distance covered by a child can be given as,
Δd = 10cm + 70 cm = 80 cm
Thus, the total distance is 80cm and a child moves back 5cm then the displacement would be given as,
Displacement = total distance cover - distance move back
Displacement = 80cm - 5 cm = 75 cm
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A periodic wave has a wavelength of 1.6 m and a speed of 16 m/s. What is the wave frequency?
ANSWER
10 Hz
EXPLANATION
Given:
• The wavelength of a periodic wave, λ = 1.6 m
,• Its speed, v = 16 m/s
Find:
• The wave frequency, f
The frequency of a wave is given by the quotient between the wave's speed and its wavelength,
[tex]f=\frac{v}{\lambda}[/tex]Replace the known values and solve,
[tex]f=\frac{16m\/s}{1.6m}=10\text{ }\frac{1}{s}=10\text{ }Hz[/tex]Hence, the frequency of the wave is 10 Hz.
while riding a roller coaster, a girl drops an object. the roller coaster was rising vertically at a velocity of 11.0m/s and was 5.00m above the ground when the object was dropped. how long does it take to reach the ground
Answer:
Approximately [tex]0.388\; {\rm s}[/tex], assuming that air resistance is negligible and that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].
Explanation:
Initial vertical velocity of the object: [tex]u = 11.0\; {\rm m\cdot s^{-1}}[/tex], upwards (same as that of the rollercoaster.)
Initial height of the object: [tex]h_{0} = 5.00\; {\rm m}[/tex].
If air resistance is negligible, this object will accelerate downwards at a constant [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex]. Note that [tex]a[/tex] is negative since the object is accelerating downwards.
The SUVAT equation [tex]h = (1/2)\, a\, t^{2} + u\, t + h_{0}[/tex] gives the height [tex]h[/tex] of this object at time [tex]t[/tex]. Note that while the initial height is [tex]5.00\; {\rm m}[/tex], [tex]h = 0[/tex] when the object reaches the ground.
Since acceleration [tex]a[/tex], initial velocity [tex]u[/tex], and initial height [tex]h_{0}[/tex] are all given, setting [tex]h\![/tex] to [tex]0[/tex] and solving for [tex]t[/tex] will give the time it takes for this object to reach the ground:
[tex](1/2)\, a\, t^{2} + u\, t + h_{0} = 0[/tex].
[tex](1/2)\, (-9.81) \, t^{2} + 11.0\, t + 5.00 = 0[/tex].
[tex](-4.905)\, t^{2} + 11.0\, t + 5.00 = 0[/tex].
Solve this equation for [tex]t\![/tex] using the quadratic formula. Note that [tex]t > 0[/tex] since [tex]t[/tex] denotes the amount of time required for the object to reach the ground.
[tex]\begin{aligned} t &= \frac{-11.0 + \sqrt{11.0^{2} - 4 \times (-4.905) \times 5.00}}{2\times (-4.905)} \\ &\approx 0.388\; {\rm s}\end{aligned}[/tex].
The other root of this quadratic equation is negative and isn't a valid solution to the question.
In other words, it will take approximately [tex]0.388\; {\rm s}[/tex] for this object to reach the ground.
a 28 kg child is coasting at 2.0 m/s over flat ground in a 5.0 kg wagon. the child drops a 1.1 kg ball from the side of the wagon. what is the final speed (in m/s) of the child and wagon?
The final speed of the child and wagon is 2.1 m/s.
Momentum in a simple manner is an amount of motion. here amount is measurable due to the fact if an item is transferring and has mass, then it has momentum. If an object does not pass then it has no momentum. however, in normal lifestyles, it has a significance that many human beings failed to recognize it.
mass of child = 20 kg
mass of wagon = 5 kg
total mass m₁ = 25 kg
mass of ball dropped = 1.1 kg
new mass m₂ = 23.9
the initial speed of the child and wagon u₁ = 2 m/s
the final speed of the wagon = v₂
using conservation of momentum
m₁u₁ = m₂v₂
25×2 = 23.9 × v₂
final speed v₂ = 50/23.9
= 2.092 m/s
= 2.1 m/s
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the shape of an atomic orbital is associated with group of answer choices the spin quantum number (ms). the principal quantum number (n). the angular momentum quantum number (l). the magnetic quantum number (ml). the magnetic and spin quantum numbers, together.
The shape of an atomic orbital is associated with the principal quantum number (n).
Why do atoms have orbitals?
The wave character of the electrons (or electron pairs) in an atom is described by atomic orbitals, which are mathematical functions. They provide a method for calculating the likelihood that an electron will be located in a particular area surrounding the atom's nucleus. An atom can have any number of orbitals, according to the quantum atomic model.
Why do a wave's orbitals affect the shape of the wave?The function of the wave will therefore be determined by the distance from the nucleus and not by its direction. Any particle's orbital shrinks in size but maintains a spherical geometry as its center quantum number drops.
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An engineer is troubleshooting trying to figure out the value of a capacitor. She knows that the charge value is 480 coulombs and the power supply feeds 110 V. What's the capacitor value?Question 19 options:A) 128B) 4.36C) 0.88D) 5,400
We can use the formula of the capacitance
[tex]C=\frac{Q}{V}[/tex]where C is the capacitance, Q is the charge and V is the voltage.
In our case
Q=480 C
V= 110 V
[tex]C=\frac{480}{110}=4.36\text{ F}[/tex]The value of the capacitor is 4.36 F
ANSWER B) 4.36F
Reflect on the claims and the evidence you examined today. At this point, which claim do you think is best supported by the evidence?
Claim 1: There is frozen water in tank 2, which is blocking some of the oxygen from going into tank 3.
Claim 1: , There is frozen water in tank 2, which is blocking some of the oxygen from going into tank 3.
Claim 2: Some of the liquid oxygen evaporated in tank 3.
Claim 2:, Some of the liquid oxygen evaporated in tank 3.
Claim 3: Some of the oxygen didn’t condense in tank 2.
Claim 3:, Some of the oxygen didn’t condense in tank 2.
In the space below, explain your claim choice using the evidence you discussed today.
Claim 2: Some of the liquid oxygen evaporated in tank 3 is the claim with the most proof based on the experiment with liquid oxygen and nitrogen.
In the propellant systems of missiles and rockets, liquid oxygen is employed as an oxidant for liquid fuels. In addition to acetylene and other fuel gases, oxygen is frequently used in the metal industry for metal cutting, welding, scarfing, hardening, cleaning, and melting.Therefore, the reason of above statement can be explained as, that nitrogen has a lower boiling point than oxygen, the liquid nitrogen and oxygen mixture in tank 3 is slightly heated to allow nitrogen to escape. However, as gas particles can evaporate at a temperature below their boiling point provided they have enough energy, some oxygen might have escaped simultaneously when the boiling produced sufficient energy.
Thus the claim 2 is suitable option of this evidence.
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Your friend wants to place an object behind the mirror to prevent the eye from seeing the image in the
mirror. Explain why this won't work.
According to the law of reflection, the light from the item cannot bounce off the mirror and reach his eye across his line of sight.
Briefing:According to the law of reflection, the light from the item cannot bounce off the mirror and reach his eye across his line of sight. Ray is unable to see the object's reflection in the mirror because the object's light does not reach his eye.
What is law of reflection ?The law of reflection, the angle of the reflected beam is equal to the angle of the incident ray while reflecting from a smooth surface. (In geometrical optics, all angles are usually measured in relation to the surface normal, or a line perpendicular to the surface.
How is the law of reflection used?In physics, the rule of reflection is used to locate an image that is reflected in a mirror. One effect of a law is that if you can see someone's eyes through a mirror (or the eyes of another species), you can assume that he may see your eyes as well because of how reflection function.
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Just before Sarah started her laboratory work, she made a hot cup of tea. She left the tea on her desk while she worked because she never takes food or drink into the lab area. When she finished collecting data, Sarah's cup of tea was cool. What energy transfer caused her tea to cool?
The energy transfer between cup tea and surrounding caused her tea to cool according to newtons law of cooling.
The pace at which a body is exposed to radiation alters its temperature is roughly proportional to the temperature difference between the item and its surroundings, and the provided difference is small. The cooling law of Newton is this.
Heat is transported more quickly and a person's body temperature changes more quickly the higher the temperature difference between a system and its surroundings. When the temperature difference between the body and its surroundings is small, the rate of cooling of a body is directly related to the temperature difference and the surface area exposed.
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what is the momentum of an 7.2- kgkg bowling ball rolling at 3.0 m/sm/s ? express your answer to two significant figures and include the appropriate units.
Answer: 20.16kg.m\s
Explanation: Here is given that M= 7.2 Kg, and v= 2.8 m/s So, momentum ,P=M. v = (7.2*2.8) = 20.16 Kg. m/s, which is a number having four significant digits. but we have to provide the answer in two significant digits. Therefore, to convert
a horizontal rifle is fired at a bull's-eye. the muzzle speed of the bullet is 655 m/s. the gun is pointed directly at the center of the bull's-eye, but the bullet strikes the target 0.029 m below the center. what is the horizontal distance between the end of the rifle and the bull's-eye?
The horizontal distance between the end of the rifle and the eye of the bull is equal to 50.35 m.
What are the equations of motion?The equations of motion can be described as the equations which set up the relationship between the velocity of the object, the acceleration, time, and distance of the moving object.
Consider that a vector r, which describes the position of the bullet when it reaches the target, is composed of [tex]r_x[/tex] and [tex]r_y[/tex]
[tex]r = (r_x, r_y)[/tex]
Given that [tex]r_y[/tex] is -0.029 m (the reference is located at the end of the rifle),
r =([tex]r_x[/tex], -0.029 m)
The vertical position of the bullet at time 't' can be written in form of an equation as follows:
[tex]y = (y_o +v_oy) t + \frac{1}{2} g t^2[/tex]
The vertical component of the speed at t = 0 is 0, then, acceleration, v₀y = 0 and y₀ = 0.
Then, we can find the time for the vertical position (y) of bullet -0.029 m:
-0.029 m =(0)t - (1/2) · (9.8 m/s²) · t²
t = 0.077 sec
The equation for the horizontal position can be written as:
x = x₀ + (v₀x) · t
Since the origin of the reference system is located at the bullet starts its trajectory, x₀ = 0.
x = (v₀x) · t
x = (655) × 0.077 = 50.35m
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