Explanation:
Average Speed=Distance/Time
=(10+5)/20
=15/20=0.75cm/s
Average velocity = Displacement/Time
= (10-5)/20 cm/s
= 5/20m/s = 0.25cm/s
which lobes of the brain receive the input that enables
The input that enables humans to feel sensations of touch and pressure is received by the parietal lobes of the brain.
The parietal lobes are responsible for processing sensory information, including touch, pressure, temperature, and pain. The sense of touch is detected by specialized receptors located in the skin, muscles, and other tissues throughout the body. These receptors send signals through the spinal cord to the parietal lobes of the brain, where they are processed and interpreted to create the sensation of touch.
The parietal lobes of the brain are involved in processing sensory information, including touch, pressure, temperature, and pain. The sense of touch is detected by specialized receptors located in the skin, muscles, and other tissues throughout the body. These receptors send signals through the spinal cord to the parietal lobes of the brain, where they are processed and interpreted to create the sensation of touch. The somatosensory cortex is a region of the parietal lobes that are responsible for processing sensory information from different parts of the body. The somatosensory cortex is organized into a map-like representation of the body, known as the somatosensory homunculus. This map allows the brain to interpret sensory information from different parts of the body and create a coherent perception of the physical world. The parietal lobes also play a role in spatial awareness and perception. They are involved in coordinating movements and integrating sensory information from different senses to create a unified perception of the environment. Damage to the parietal lobes can result in deficits in sensory perception, spatial awareness, and body awareness.
In conclusion, the parietal lobes of the brain receive the input that enables humans to feel sensations of touch and pressure. The somatosensory cortex, a region of the parietal lobes, is responsible for processing sensory information from different parts of the body and creating a coherent perception of the physical world. The parietal lobes also play a role in spatial awareness and perception and are involved in coordinating movements and integrating sensory information from different senses.
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which of the following is correct regarding collision theory? group of answer choices all molecular collisions result in chemical reactions. reaction rates always decrease when reactant concentrations decrease, because lower concentration results in lower collision frequency. catalysts speed up reactions because catalysts can increase the kinetic energy of reactants. higher temperature increases the frequency of effective collision.
The correct statement regarding collision theory is:
Higher temperature increases the frequency of effective collision.
According to collision theory, for a chemical reaction to occur, molecules must collide with sufficient energy and proper orientation. Increasing the temperature increases the kinetic energy of the molecules, leading to higher collision frequencies and a greater likelihood of successful collisions. Therefore, higher temperatures increase the frequency of effective collisions and can accelerate the reaction rate.
The other statements are not entirely accurate:
1. Not all molecular collisions result in chemical reactions. The collisions must occur with sufficient energy and proper orientation for a reaction to take place.
2. The reaction rates do not always decrease when reactant concentrations decrease. In some cases, the reaction rate may depend on the concentration of certain reactants, but it is not a general rule.
3. Catalysts speed up reactions by providing an alternative reaction pathway with lower activation energy, allowing the reaction to proceed at a faster rate. Catalysts do not increase the kinetic energy of reactants.
Hence, The correct statement regarding collision theory is Higher temperature increases the frequency of effective collision.
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A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at 40∘C at a rate of 850m3/min and leaves the turbine at 650∘C. Assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine
(a) the net power output,
(b) the back work ratio, and
(c) the thermal efficiency.
Use constant specific heats with
cv=0.821kJ/kg?
K,cp=1.108kJ/kg?
K, and k=1.35.
Answer:
a) 6498.84 kW
b) 0.51
c) 0.379
Explanation:
See the attached picture below for the solution
Given-
Temperature at state 1 \(T_{1}\) is 40 degree cel. This is equal to the 313 K.
Temperature at state 1 \(T_{2}\) is 650 degree cel. This is equal to the 923 K.
To know the mass flow rate use the idol gas equation. Idol gas equation for a substance can be given as,
\(PV=nRT\)
Rewrite this equation for \(n\),
\(n=\dfrac{PV}{RT}\)
Put the value of known variable from the question,
\(n=\dfrac{100\times\dfrac{850}{60} }{0.287\times 313}\)
\(n=15.77\)
Thus the value of n is 15.77 kg/sec.
Temperature at state 2 is,
In Bryon cycle we know that the processes 1-2 and 3-4 are isotropic. Hence,
\(T_{2} =T_{1}\left (1+ \dfrac{r_{p}^{\dfrac{\gamma-1}{\gamma}-1} }{c_{v} } \right )\)
\(T_{2} =313\left (1+ \dfrac{16^{\dfrac{1.35-1}{1.35}-1} }{0.821 } \right )\)
\(T_{2} =700\)
Temperature at state 3 is,
\(T_{3} =\dfrac{T_4}{1+c_p(r_p^{\dfrac{\gamma-1}{\gamma}-1}-1)}\)
Put the value in above equation we get,
\(T_3=1682\)
Net power output is,\(W=mc_p(T_i{n}-T_{out})\)
\(W=mc_p(T_3-T_2-T_4+T_{1})\)
\(W=15.77\times1.109(1682-700-923+313)\)
\(W=65\)
Thus the net power output is 70 watt.
The back work ratio,
\(r_b=\dfrac{T_2-T_1}{T_3-T_4}\)
\(r_b=\dfrac{700-313}{1682-923}\)
\(r_b=0.51\)
Hence the back work ratio is 0.51.
The thermal efficiency-\(\eta=\dfrac{W}{Q_{in}}\)
\(\eta=\dfrac{65}{mc_p(T_3-T_2)}\)
\(\eta=0.379\)
Hence, for the given problem the net power output is 70 watt,the back work ration is 0.51, and the thermal efficiency is 0.379.
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In a sugar factory bagasse (the remains of the cane after the juice is extracted) is burned to provide electricity. The types of energy involved are W thermal energy X chemical energy Y electrical energy Z kinetic energy. In what order are these forms of energy converted in this process?A) WXZYB) XWZYC) WZXYD ZXWY
Given:
Thermal energy is denoted by W
Chemical energy is denoted by X
Electrical energy is denoted by Y
Kinetic energy is denoted by Z
To find the order of energy while converting bagasse to electricity.
Explanation:
The bagasse has chemical energy stored in it.
The bagasse is burned, so chemical energy gets converted into thermal energy.
The thermal energy gets converted into kinetic energy.
The kinetic results in the motion of electrons.
Thus, producing electrical energy.
Hence, the conversion order is XWZY
two point charges exert a 8.05 n force on each other. what will the force become if the distance between them is increased by a factor of 2?
When the distance between two point charges is increased by a factor of 2, the force they exert on each other decreases to 1/4 of the original force. The relation is governed by the Coulomb's Law.
According to Coulomb's Law, the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this scenario, if the distance between the charges is increased by a factor of 2, it means that the new distance is twice the original distance.
Since the force is inversely proportional to the square of the distance, doubling the distance will result in the force becoming 1/4 of the original force. Mathematically, this can be represented as follows:
\(F' = F / (2^2)\)
\(F' = F / 4\)
Therefore, the force between the two charges will become 1/4 (or 25%) of the original force when the distance between them is increased by a factor of 2.
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You push a 13‑kg table in the cafeteria with a horizontal force of 20 N, but the table does not move. You then push the table with a horizontal force of 25 N, and it accelerates at 0.26 m/s2. What, if anything, can you conclude about the coefficients of static and kinetic friction?
The coefficient of static fiction is 0.15 and the coefficient of kinetic friction is 0.19
What is coefficient of static and kinetic friction?Coefficient of static friction is the maximum ratio of applied force to normal force with no motion. We all know Frictional force is a force which opposes motion. Coefficient of static friction of the table is :
coefficient of static friction = applied force/normal reaction
applied for when it's stable = 20N
normal reaction = m×g = 13× 10= 130N
therefore the coefficient of static friction = 20/130 = 0.15
The coefficient of kinetic friction (μk) is the ratio of the friction force to the normal force experienced by a body moving on a dry, non-smooth surface.
μk = moving force/ normal reaction
therefore μk = 25/130
μk = 0.19
therefore the coefficient of kinetic friction is 0.19
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Please help.
Lions used to hunt by themselves. Now, they hunt in packs. What type of adaptation is this?
A.structural adaptation
B.behavioral adaptation
C. functional adaptation
Answer:
I think it is behavioral
If the entire chart represents 100 homes, how many households have a pet bird?
A. cannot be determined
B. 1
C:50
D.10
Answer:
where is the chart.?
the chart is needed in order to get the answer accurately
match the letter with the layer
Answer:
Thermosphere A,B
Mesosphere B,C,D
Stratosphere D,E,F
Troposphere G
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calculate the braking distance traveled as the speed of the car is reduced from 21 m/s to 0m/s
The braking distance traveled by the car is 73.5 m.
What is the braking distance of the car?The braking distance traveled as the speed of the car is reduced from 21 m/s to 0m/s at a deceleration rate of 3 m/s² is calculated as follows.
v² = u² - 2as
where;
v is the final velocity of the car, when it stops = 0u is the initial velocity of the car = 21 m/sa is the deceleration of the car = 3 m/s²s is the braking distance of the carSubstitute the given parameters and solve for the braking distance of the car as shown below.
0 = u² - 2as
2as = u²
s = (u²) / (2a)
s = (21²) / (2 x 3)
s = 73.5 m
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The complete question is below:
calculate the braking distance traveled as the speed of the car is reduced from 21 m/s to 0m/s, when the car is decelerating at 3 m/s².
Which of the following is BOTH an isotope and ion of Chlorine? plz help
a
B
c
D
Answer:
The answer is C.
Explanation:
because if you look ay the nutrons you can see that it adds to the protons
Answer:
C
Explanation:
Isotopes of Chlorine (Cl) gain an electron when they form ionic bonds. This results in a negative ion (the Chloride ion). ... When the charge on an atom is zero it means the number of protons is equal to the number of electrons. The atom is said to be neutral and there will not be a + or - written after the element symbol.
What is the acceleration?
Answer: \overline {a} = {v - v_0}{t} = \frac{\Delta v}{\Delta t}
\overline{a} = average acceleration
v = final velocity
v_0 = starting velocity
t = elapsed time
Explanation: math i hoped it helped.
Answer:
3m/s2
Explanation:
By using the equation
F=ma
For calculating acceleration the eq will be
a=f/m
a=6/2
a=3
Which is not a typical property of an acid?
A They react with alkalis producing water.
B They react with all metals producing hydrogen.
C They react with carbonates producing carbon dioxide.
D They turn litmus paper red.
Answer:
B They react with all metals producing hydrogen.
Twenty (20.0) mL of argon gas (Ar) is stored at STP. If the temperature and pressure are both doubled, what is the new volume?
PLZZ ANSWER ASAP!!
Answer:
The new volume is the same as the initial volume, i.e. 20 mL.
Explanation:
To find the new volume we can use the Ideal gas law:
\( PV = nRT \)
Where:
P: is the pressure
V: is the volume
R: is the gas constant
n: is the number of moles
T: is the temperature
Initially, we have:
\( \frac{P_{i}V_{i}}{T_{i}} = nR \) (1)
In the final state:
\( \frac{P_{f}V_{f}}{T_{f}} = nR \) (2)
By equating equation (1) and (2) we have:
\( \frac{P_{i}V_{i}}{T_{i}} = \frac{P_{f}V_{f}}{T_{f}} \)
\( \frac{P_{i}V_{i}}{T_{i}} = \frac{2P_{i}V_{f}}{2T_{i}} \)
\(V_{f} = \frac{2T_{i}*P_{i}*V_{i}}{T_{i}*2P_{i}}\)
\( V_{f} = V_{i} \)
\( V_{f} = 20.0 mL \)
Therefore, the new volume is the same as the initial volume, i.e. 20 mL.
I hope it helps you!
6. Which phase of matter has a definite volume and shape.
a. solid
b. liquid
c. gas
d.plasma
Answer:
solids
Explanation:
beacause if you take an ice cube does it change its shape no and if it has a definite shape it is sure to have a definite volume
6th grade science please help
How do you think population variables would affect the economic impact of an environmental hazard?
Effects of Population Growth on The Economy Population growth may have a positive effect on the economy.
How does population affect the economy?Human population growth bounces the Earth's system in a variety of ways, involving Increasing the extraction of resources from the environment. Rapid population growth built it more difficult for low-income and lower-middle-income countries to supply the increase in public expenditures. Population growth, along with increasing use, of the economy tends to increase emissions of climate-changing greenhouse gases.
On a facile level, the relationship between growth in population and growth in per capita income is clear. After all, per capita income equals total income divided by population. The growth rate of per capita income forcefully equals the difference joining the growth rate of income and the growth rate of population.
So we can conclude that Population size, growth, age structure, and geographic issues influence economies.
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the mass is increased by a factor of four, keeping a and k constant. what is true about the total mechanical energy? choose the best answer.
When the mass is increased by a factor of four, keeping a and k constant mechanical energy increases by a factor of 4.
When mass is twice, what happens to the spring constant?The mass that is linked to the spring has no bearing on its force constant. As a result, it remains unchanged by the attached mass.
If the force is doubled and the mass remains constant, what will happen to the acceleration?The acceleration of an object rises proportionally to the force applied to it. We can state that force and acceleration are identical because the mass does not change when the acceleration rises. So, doubling the force also doubles the acceleration.
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Two celestial bodies in outer space collide. one of the celestial bodies has a mass of 55 kg with a velocity of 565 m/s, while the other has a mass of 40 kg and a velocity of 613 m/s west. what is the final velocity? show all calculations out!
To calculate the final velocity after the collision between the two celestial bodies, we need to apply the principle of conservation of momentum. The final velocity will depend on the masses and initial velocities of the bodies.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is given by the product of its mass and velocity.
Let's denote the mass of the first celestial body as m1 (55 kg) with a velocity of v1 (565 m/s), and the mass of the second celestial body as m2 (40 kg) with a velocity of v2 (-613 m/s, since it is moving west).
The total momentum before the collision is given by:
Initial momentum = m1 * v1 + m2 * v2
To find the final velocity, we need to equate the initial momentum to the total momentum after the collision:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
Where vf represents the final velocity.
Solving this equation for vf, we get:
vf = (m1 * v1 + m2 * v2) / (m1 + m2)
Substituting the given values, we have:
vf = (55 kg * 565 m/s + 40 kg * -613 m/s) / (55 kg + 40 kg)
vf = (-2905 kg·m/s) / (95 kg)
vf ≈ -30.58 m/s
Therefore, the final velocity after the collision is approximately -30.58 m/s. The negative sign indicates that the final velocity is in the opposite direction of the initial velocities.
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a burning candle is placed 20cm in front of a concave mirror of focal length 10cm find the nature and position of the image formed
real and inverted same size
the weight of the atmosphere above 1 m2 of earth's surface is about 100,000 n. density, of course, becomes less with altitude. but suppose the density of air were a constant 1.2 kg/m3.
The thickness of the air column above 1 m² of the Earth's surface that would have a weight of about 100,000 N is equal to 8,680.56 meters assuming the density of air remained constant at 1.2 kg/m³.
If the density of air were a constant 1.2 kg/m³ throughout the atmosphere, we can calculate the thickness of the air column that would have a weight of about 100,000 N on an area of 1 m².
The weight of the air column can be calculated using the formula:
Weight = density × volume × gravitational acceleration
We can rearrange the formula to solve for the volume:
\(\text{{Volume}} = \frac{{\text{{Weight}}}}{{\text{{density}} \times \text{{gravitational acceleration}}}}\)
Substituting the given values:
Weight = 100,000 N
Density = 1.2 kg/m³
Gravitational acceleration (g) ≈ 9.8 m/s²
\(Volume = \frac{100000 N}{(1.2 kg/m^3) \times (9.8 m/s^2)}\)
Volume ≈ 8,680.56 m³
Therefore, if the density of air were a constant 1.2 kg/m³, the thickness of the air column above 1 m² of the Earth's surface that would have a weight of about 100,000 N is approximately 8,680.56 meters.
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1. A cello string 0.75 m long has a fundamental frequency of 220 Hz. The speed of a wave on this string is
a) 165 m/s
b) 220 m/s
c) 294 m/s
d) 330 m/s
The speed of a wave on a cello string 0.75 m long that has a fundamental frequency of 220 Hz is (d) 330 m/s.
The speed of the wave on the string can be calculated using the formula;v = fλwhere:v = speed of the wave in m/sf = frequency of the wave in
Hzλ = wavelength of the wave in m
Calculating wavelength from fundamental frequency
We know that the fundamental frequency of a string is given by:
f1 = v / 2L
where:f1 = fundamental frequency of the string, v = speed of the wave in the string, L = length of the string
Therefore:
λ1 = 2L / 1λ1 = 2L
Calculating wavelength from second harmonic frequency.
The second harmonic of a string is the frequency that produces two complete waves in the string. It can be obtained from the formula:
f2 = 2f1
where: f2 = second harmonic frequency, f1 = fundamental frequency.
Substituting the value of f1 into the equation:
f2 = 2v / 2L = v/Lλ2 = L.
Calculating wavelength from third harmonic frequency.
The third harmonic of a string is the frequency that produces three complete waves in the string. It can be obtained from the formula:
f3 = 3f1
where: f3 = third harmonic frequency, f1 = fundamental frequency.
Substituting the value of f1 into the equation:
f3 = 3v / 2Lλ3 = 2L/3
Calculating the speed of the wave from the wavelength and frequency.
Substituting the calculated wavelength of the first harmonic into the equation for the speed of the wave:
v = f1λ1v = 220 × 2(0.75)
Therefore:v = 330 m/s
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Stored digital data are easily changed. How could this be a disadvantage?
A. Changing data results in too much data to be stored in most
computers
B. Easily changed data are difficult to protect with a security system.
c. Once a change is made, the change is permanent.
D. True information in the digital data can be changed to false
information
SUBMIT
I need help on this
The disadvantage of easily changeable digital data is: true information in the digital data can be changed to false information. Hence, option (D) is correct.
What is digital data?Digital data, in information theory and information systems, is information represented as a string of discrete symbols, each of which can take on one of only a finite number of values from some alphabet, such as letters or digits.
An example is a text document, which consists of a string of alphanumeric characters. The most common form of digital data in modern information systems is binary data.
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Answer: The answer is D.
Explanation: I took the test
The velocity – time graph of an object moving along a straight line is shown in
fig. Find (a) the distance covered and (b) the displacement of the object in time
interval between t = 0 s and t = 10 s
(a) The distance travelled by the object is 100 m.
(b) The displacement of the object in time interval between t = 0 s and t = 10 s is 60 m.
What is the distance covered by the object?(a) The distance travelled by the object is calculated from the total area of the curve.
total distance = area of triangle 1 + area of triangle 2 + area of rectangle.
total distance = (¹/₂ x base x height)₁ + (¹/₂ x base x height)₂ + length x width
total distance = (¹/₂ x 6 s x 20 m/s) + (¹/₂ (8 - 6) 20) + (10 - 0)(10 - 8)
total distance = 60 m + 20 m + 20 m
total distance = 100 m
(b) The displacement of the object in time interval between t = 0 s and t = 10 s is calculated as follows;
displacement = final position - initial position
displacement = (¹/₂ x base x height)₁ + (¹/₂ x base x height)₂ + length x width
displacement = (¹/₂ x 6 s x 20 m/s) + (¹/₂ (8 - 6) (-20)) + (10 - 0)(10 - 8)
displacement = 60 m - 20 m + 20 m = 60 m
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Question:Which of the following statements is true?a. State functions do not depend on the path taken to arrive at a particular state.b. Energy is neither created nor destroyed, excluding nuclear reactions.c. ΔHrxn can be determined using constant pressure calorimetry.d. ΔErxn can be determined using constant volume calorimetry.e. All of the above are true.State or Path Functions:The state functions are the variable such as density, pressure, etc. that are calculated by subtracting initial values from final values. Path function necessarily relies on the path followed. In thermodynamics, only two heat and work are depicted as path functions.
Statement (e), "All of the above are true," is true.
State functions do not depend on the path taken to arrive at a particular state. Energy is a state function and it is conserved, meaning it is neither created nor destroyed, excluding nuclear reactions. ΔHrxn, the change in enthalpy, can be determined using constant pressure calorimetry, which measures the heat flow into or out of a system at constant pressure. ΔErxn, the change in internal energy, can be determined using constant volume calorimetry, which measures the heat flow into or out of a system at constant volume. In thermodynamics, state functions, such as enthalpy, internal energy, and entropy, are defined by their values at a particular state and are not dependent on the path taken to arrive at that state. On the other hand, heat and work are considered path functions because they depend on the path taken to arrive at a particular state.To know more about thermodynamics visit:
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A 0.5-kg ball moving at 5 m/s strikes a wall and rebounds in the opposite direction with a speed of 2 m/s. If the impulse occurs for a time duration of 0.01 s, find the magnitude of the net force on the ball.
Answer: 350 N
Explanation:
Given
Mass of ball is \(0.5\ kg\)
Speed of ball after rebound is \(v=2\ m/s\)
Time period for impulse \(t=0.01\ s\)
Impulse imparted in equal to the change in the momentum of object
\(\Rightarrow J=m(v-u)\quad [\text{u=speed of ball before collision}]\\\Rightarrow J=0.5\times \left(2-(-5)\right)\\\Rightarrow J=0.5\times 7\\\Rightarrow J=3.5\ N.s\)
Impulse is the product of average force and duration of application
\(\Rightarrow J=F_{avg}\cdot \Delta t\\\Rightarrow 3.5=F_{avg}\times 0.01\\\\\Rightarrow F_{avg}=350\ N\)
Waves start as a disturbance (an input of energy) in a medium (water, air, the earth etc). The energy of the disturbance is moved from the starting point to other places in the medium by what means
A surge is a nonstop and repeating disturbance of a medium and a palpitation is a single disturbance.
What's surge?
A surge is a disturbance that propagates through a medium. There are three words in that description that may need discharging disturbance, propagate, and medium.
A disturbance, in the sense used in this description, is a change from the current state of a measurable volume at some position. For illustration
a change in a kinematic variable like position, haste, or acceleration;
a change in an ferocious property like pressure, viscosity, or temperature;
a change in field strength like electric field strength, glamorous field strength, or gravitational field strength.
To propagate, in the sense used in this description, is to transmit the influence of commodity in a particular direction. Antonyms for propagate include spread, transmit, communicate, and broadcast. The noun form of the word is propagation.
A medium is the substance through which a surge can propagate. Water is the medium of ocean swells. Air is the medium through which we hear sound swells. The electric and glamorous fields are the medium of light. People are the medium of a colosseum surge. The Earth is the medium of seismic swells( earthquake swells). Cell membranes are the medium of whim-whams impulses. Transmission lines are the medium of interspersing current electric power. Medium is the form of the noun. Media is the plural form( although mediums is by some people).
Let's list a many crucial exemplifications of surge marvels and also connect them to this description. The first illustration that comes to mind when utmost people hear the word surge are the kinds of swells that one sees on the face of a body of water deep water swells in the ocean or ripples in a billabong
. The most important kinds of swells for humans are the swells we use to smell the world around us sound and light.
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If the surface becomes smaller the pressure becomes
Answer:
Greater
Explanation:
Have a nice day
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Answer:
if the surface becomes smaller, the pressure becomes larger,
A physics teacher is desperate to break his students
of a physics misconception. To do this, he drops a
book from a height of 1.4 m. How fast is the book
going when it hits the ground?
If a book is drops from a height of 1.4 m, then the speed with which book hits the ground is 5.2 m/s.
Given,
Initial velocity = 0m/s
Height = h = 1.4m
Acceleration due to gravity = 9.8 m/s2.
This can be calculated by using third equation of motion,
v2 - u2 = 2gh
where,
v is the final velocity
u is the initial velocity
h is the height
and g is the acceleration due to gravity.
By substituting all the values, we get
v2 = 2 × 1.4 × 9.8
v2 = 27.44
v = 5.2 m/s
Thus, we concluded that if a book is drops
from a height of 1.4 m, then the speed with which book hits the ground is 5.2 m/s.
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what additional property of observable (hermitian) operators is assumed (not proved) so that quantum mechanics will make sense?
The additional property assumed for observable (hermitian) operators in quantum mechanics is that they have a complete set of eigenvalues and corresponding eigenvectors.
In quantum mechanics, observables are represented by hermitian operators, which have real eigenvalues and orthogonal eigenvectors. The additional assumption that these operators have a complete set of eigenvalues and corresponding eigenvectors is necessary to ensure that any state of a system can be expressed as a linear combination of the eigenvectors. This is known as the spectral theorem, and it allows us to measure the observable values of a system with certainty. Without this assumption, quantum mechanics would not make sense as we would not be able to determine the state of a system accurately.
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