Answer:
a) Both stones hit at the same time, b) Stones A and B will land at a distance of \(2.26\sqrt{y_{o}}\) and \(0.452\sqrt{y_{o}}\) meters, respectively.
Explanation:
Each stone experiments a parabolic motion, that is, the combination of a horizontal motion at constant velocity and a vertical uniform accelerated motion due to gravity. We know that each stone is launched horizontally at the same height and from the same initial position.
The equations of motion for each stone are described below:
Stone A
\(x_{A} = x_{o} + v_{A,o}\cdot t_{A}\)
\(0 = y_{o} + \frac{1}{2}\cdot g\cdot t_{A}^{2}\)
Stone B
\(x_{B} = x_{o} + v_{B,o}\cdot t_{B}\)
\(0 = y_{o} + \frac{1}{2}\cdot g\cdot t_{B}^{2}\)
a) Which stone hits the ground first?
The stone that hits the ground first has the lowest time. If we know that \(v_{A,o} = 5\,\frac{m}{s}\), \(v_{B,o} = 1\,\frac{m}{s}\), \(x_{o} = 0\,m\) and \(g = -9.807\,\frac{m}{s^{2}}\), then the equations of motion are reduced into this:
Stone A
\(x_{A} = 5\cdot t_{A}\) (Eq. 1)
\(y_{o} -4.905\cdot t_{A}^{2}= 0\) (Eq. 2)
Stone B
\(x_{B} = t_{B}\) (Eq. 3)
\(y_{o} -4.905\cdot t_{B}^{2}= 0\) (Eq. 4)
From (Eq. 2) and (Eq. 4), we get that \(t_{A} = t_{B}\).
Both stones hit at the same time.
b) Where do they land?
From (Eq. 2) and (Eq. 4), we get:
\(y_{o} = 4.905\cdot t^{2}\)
The time is cleared within the expression:
\(t =\sqrt{\frac{y_{o}}{4.905} }\)
\(t \approx 0.452\sqrt{y_{o}}\)
And from (Eq. 1) and (Eq. 3), we get the following equations of motion:
\(x_{A}= 5\cdot t\)
\(x_{B} = t\)
The horizontal distance taken by each stone is calculated by direct substitution on each expression:
\(x_{A} = 2.26\sqrt{y_{o}}\,m\)
\(x_{B} = 0.452\sqrt{y_{o}}\,m\)
Stones A and B will land at a distance of \(2.26\sqrt{y_{o}}\) and \(0.452\sqrt{y_{o}}\) meters, respectively.
Why does frost bite occur in mountain climbers ?
Answer:
Because they are in places that may be extremely cold
Explanation:
For example take Mount Everest. This place is a very high mountain, and is very cold. Usually hikers would get a frost bite from how cold it is in there. According to google, "Frostbite is an injury caused by freezing of the skin and underlying tissues."
A hanging wire made of an alloy of magnesium with diameter 0.08 cm is initially 2.0 m long. When a 12 kg mass is hung from it, the wire stretches an amount 1.17 cm. A mole of magnesium has a mass of 24 grams, and its density is 1.74 g/cm3.Based on these experimental measurements, what is Young's modulus for this alloy of magnesium
The Young's modulus for the alloy of magnesium is approximately 1.01 × 10^10 N/m².
What is the value of Young's modulus for this alloy of magnesium?Young's modulus is a measure of the stiffness of a material and represents its ability to resist deformation under stress.
To calculate Young's modulus for the given alloy of magnesium, we need to use Hooke's Law, which states that the stress applied to a material is directly proportional to the strain it produces.
First, we calculate the strain of the wire using the formula:
\(strain = change\ in\ length / original\ length\)
In this case, the wire stretches by 1.17 cm, so the change in length is 0.0117 m. The original length of the wire is 2.0 m.
Next, we calculate the stress applied to the wire using the formula:
\(stress = force / cross-sectional\ area.\)
The force applied to the wire is the weight of the 12 kg mass, which is 12
kg × 9.8 m/s² = 117.6 N.
The cross-sectional area of the wire is given by the formula:
\(cross-sectional\ area = \pi * (diameter/2)\²\)
Substituting the values, we find the cross-sectional area to be approximately 5.03 × 10^(-6) m².
Now, we can calculate Young's modulus using the formula:
\(Young's\ modulus = stress / strain\)
Substituting the values, we get
\(Young's modulus = 117.6 N / (5.03 * 10 \^\ (-6) m\² / 0.0117 m) \\= 1.01 * 10^10 N/m\²\)
Therefore, the approximate value of Young's modulus for the alloy of magnesium is 1.01 × 10^10 N/m².
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if the mass of a gas is doubled, how is the average kinetic energy of the gas affected for any given temperature?
The pressure also doubled when the temperature did. answer P2=2atm.
According to Gay-Lussac Law, pressure and temperature have a direct relationship: P1/T1=P2/T2.
As long as the volume is kept constant, pressure and temperature will both rise or fall together.
The pressure would also double if the temperature did. The energy of the molecules would grow with increased temperature, and more collisions would occur, increasing pressure.
Double the temperature of a sample of gas that is at STP 1 atm and 273 K.
1atm/273K=P₂/546K\sP₂=2atm
The pressure increased by the same factor as the temperature.
Why is energy necessary, and what is it?Everything we eat, drink, or use contains energy. The fundamental body functions of the body are powered and governed by energy.
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how can you account for the differences in the entropies of combination of methyl propane (-1465J/mol K) and butane (1465J/mol K)
Explanation:
The change in entropy is a measure of temperature. When the temperature of a compound or a system increases, there will be more randomness in the system.
The boiling point is directly related to the number of carbon atoms but is indirectly proportional to the branching in a hydrocarbon.
Butane and methyl propane, both have 4 carbon atoms.
But, butane has 4 carbon atoms in a straight chain while methyl propane has 3 carbon atoms in a straight chain and 1 methyl substituent which makes it a branched hydrocarbon.
Thus, the boiling point of methyl propane will be less than the butane. Likewise, the pattern in entropies will be seen.
When two horizonta forces are exerted on a cart, 600N forward and 400N backward, the cart undergoes acceleration. What additional force is needed to produce nonaccelerated motion?
To produce non-accelerated motion, an additional force of 200N is needed, exerted in the backward direction to balance the net force (600N - 400N = 200N).
When two horizontal forces are exerted on a cart, 600N forward and 400N backward, the cart undergoes acceleration. To produce nonaccelerated motion, the additional force needed would be equal and opposite to the net force acting on the cart. In this case, the net force is 200N forward (600N forward - 400N backward), so an additional force of 200N backward would be needed to produce nonaccelerated motion.
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How stars are twinkling in the sky?
Answer:
As light from a star races through our atmosphere, it bounces and bumps through the different layers, bending the light before you see it. Since the hot and cold layers of air keep moving, the bending of the light changes too, which causes the star's appearance to wobble or twinkle.
An ocean scientist plans to spend several days underwater in a submarine. Doctors on land will monitor her body to make sure she is healthy during her trip. What is one way doctors will be able to tell whether her body is healthy enough to do all her tasks while she is in the submarine?
Answer:
The doctors could see if her cells are getting the molecules they need from food and air
Explanation:
The doctors could see if her cells are getting the molecules they need from food and air. Doing so allows the doctors a general overview of how well her body's biological systems are performing since the basic necessities of the human system are food and oxygen. Therefore if the body is receiving both food and oxygen properly and distributing it properly and efficiently as well without any problems then the most likely outcome is that she is healthy enough to perform her tasks in the submarine under more pressure.
Answer:
The doctors could see if her cells are getting the molecules they need from food and air
Explanation:
will give brainlyiest what is the main need or want this wave technology meets to efficiently communicate with others to hear and see others in real time to efficiently store and share music with others to speak with and see others who are far away
Answer: To see objects surrounding more clearly
Explanation:
multiple choice
12) When you move your hand or foot, your body has converted potential energy into ________ energy.
13) When coasting while roller skating, you eventually stop due to ________.
14) A ball has 100 J of potential energy when it is on a shelf. The kinetic energy of the ball the instant it hits the floor is ________J.
12). When you move your hand or foot, your body has converted potential energy into kinetic energy.
13). When coasting while roller skating, you eventually stop due to
friction causes kinetic energy to transfer to thermal energy.
14). A ball has 100 J of potential energy when it is on a shelf. The kinetic energy of the ball the instant it hits the floor is Kinetic increases, potential decreases.
What is kinetic energy, and how is it used?Kinetic energy is the force that propels motion, which can be seen in the movement of a particle, an object, or a group of particles. A person walking, a baseball being thrown, a piece of food falling from a table, and a charged particle in an electric field are all examples of objects in motion that use kinetic energy.
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Light of wavelength 580 nm in incident on a diffraction grating. A screen is placed 2.5 m away, and the distance between the zero order and first order diffraction spots is 35 cm on the screen. How many lines per mm are etched on the diffraction grating
The diffraction grating of the light of wavelength 580 nm and a screen is placed 2.5 m away, and the distance between the zero order and first order diffraction spots is 35 cm has 31.5 lines per mm etched on it.
The formula to use in this case is:
d sin θ = mλ
Where d is the distance between adjacent lines on the diffraction grating, θ is the angle between the incident light and the diffracted light, m is the order of the diffraction (0 for the zero order, 1 for the first order, etc.), and λ is the wavelength of the incident light.
In this case, we are given λ = 580 nm, m = 1, d is the unknown we are looking for, and θ can be calculated from the geometry of the setup:
tan θ = opposite / adjacent
= (35 cm / 2) / 2.5 m
= 0.07
θ = arctan(0.07)
= 4 degrees
Now we can rearrange the formula to solve for d:
d = mλ / sin θ
= (1)(580 nm) / sin(4 degrees)
= 0.0317 mm
Finally, we can convert this to lines per mm by taking the reciprocal:
lines per mm = 1 / d
= 31.5 lines per mm
Therefore, the diffraction grating has 31.5 lines per mm etched on it.
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True or false, please help me.
Comets have two tails; a white dust tail and a bluish ion tail.
For the following elementary reaction 2br• -> br2-. The rate of consumption of the reaction and the rate of formation of product is given by which set of expression?
Answer: \(-\frac{1}{2}\times \frac{d[Br^.]}{dt}=+\frac{d[Br_2]}{dt}\)
Explanation:
Rate of a reaction is defined as the rate of change of concentration per unit time.
Thus for reaction:
\(2Br^.\rightarrow Br_2\)
The rate in terms of reactants is given as negative as the concentration of reactants is decreasing with time whereas the rate in terms of products is given as positive as the concentration of products is increasing with time.
\(Rate=-\frac{d[Br^.]}{2dt}\)
or \(Rate=+\frac{d[Br_2]}{dt}\)
Thus \(-\frac{d[Br^.]}{2dt}=+\frac{d[Br_2]}{dt}\)
what do you think will happen to Charlie now that he is smart? Explain.
PLEASE HELP ONLY 30 MINS
Answer:
your answer is 0 m/s because the object is in rest
determine how you would need to change the height of the piston to increase the pressure inside the cylinder while keeping the temperature constant?
If pressure has to be decreased the height of the piston needs to be increased which will increase volume of gas eventually decreasing the pressure.
What is pressure ?The thrust (perpendicular force on a surface) acting per unit area of a body is referred to as pressure. It can be stated mathematically as follows: Pascal is the SI unit of pressure (Pa). One Pascal is the amount of pressure one Newton of force applies to a square inch of space. Additionally, 1 P a = 1 N / m 2. In the International System of Units, pressure or stress is measured in pascals (Pa) (SI). It bears Blaise Pascal's name, a mathematician and physicist. Applied force of one newton (N) per square metre is equal to one pascal (P) (m2).
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You would like to confirm Netwon's second law by running an experiment. You decide to drop two different objects from a tall building and discover that one of the objects lands on the ground five seconds before the other object. What can you conclude?
Newton's second law is not valid because each object should experience the same force of gravity and therefore should land at the same time.
There is some other force present. This additional force is different for the two objects and accounts for the fact that the objects land at different times.
Newton's second law is not relevant in determining when an object will land on the ground.
One object must be heavier than the other and must therefore experience a greater gravitational acceleration.
Answer:
You decide to drop two different objects from a tall building and discover that one of the objects lands on the ground five seconds before the other object. What can you conclude? Newton's second law is not valid because each object should experience the same force of gravity and therefore should land at the same time.
Explanation:
You decide to drop two different objects from a tall building and discover that one of the objects lands on the ground five seconds before the other object. What can you conclude? Newton's second law is not valid because each object should experience the same force of gravity and therefore should land at the same time.
You decide to drop two different objects from a tall building and discover that one of the objects lands on the ground five seconds before the other object. What can you conclude? Newton's second law is not valid because each object should experience the same force of gravity and therefore should land at the same time.
Impulsive vs. Long-Duration Flare The X-ray flux from an X5 impulsive flare can be approximated as 5x10-4e-2 W/m², t (hours) > 0 The X-ray flux from an X1 long-duration flare can be approximated as 1x10-4 e-t/3 W/m², t (hours) > 0 Calculate the total X-ray flux in J/m² for each flare. If the total fluxes are similar, which flare is more likely to signal the beginning of a significant space weather event? Why?
The X₅ impulsive flare has a total X-ray flux that is four times greater than the X1 long-duration flare.
How to calculate the valueThe total X-ray flux for the X5 impulsive flare is:
5x10-4e⁻² W/m² * 3600 s/hour * 1 hour
= 5.4 J/m²
The total X-ray flux for the X1 long-duration flare is:
1x10⁻⁴ e-t/3 W/m² * 3600 s/hour * 1 hour
= 1.2 J/m²
As you can see, the X₅ impulsive flare has a total X-ray flux that is four times greater than the X1 long-duration flare. Therefore, the X impulsive flare is more likely to signal the beginning of a significant space weather event.
The reason for this is that the X₅ impulsive flare is a much more powerful event. It releases a much larger amount of energy in a much shorter period of time.
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John added 150 grams of salt to 2.5 liters of water. what is the concentration of the salt solutions
consider a system of particles interacting with each other through potentials depending only on the scalar distances between them and acted upon by conservative central forces from a fixed point. obtain the hamiltonian of the particle with respect to a set of axes, with origin at the center of force, which is rotating around some axis in an inertial system with angular velocity w. what is the physical significance of the hamiltonian in this case? is it a constant of the motion?
The Hamiltonian of a system defines its total energy, which is the product of its kinetic energy (that of motion) and potential energy (that of position). No, it is not a constant of motion.
Lagrangian and Hamiltonian definitionsThe distinction between kinetic and potential energy is what gives rise to lagrangian. The Italian mathematician discovered the Lagrangian in the year 1788. Cartesian coordinates are a lagrangian representation. The mathematically sophisticated version of classical mechanics is known as the Hamiltonian.
Hamiltonian mechanics can also be used to derive the radial force formula. The Hamiltonian is denoted by the following in polar coordinates:
The conjugate momentum of the azimuthal angle, p, is a constant of the motion because it does not appear in the Hamiltonian. The Hamiltonian equation of motion for demonstrates that this conjugate momentum is the magnitude L of the angular momentum.
dφ/dt = δH/δpφ = pφ/mr² = L/mr²
The motion equation for r that corresponds to this is
dr/dt = δH/δpr = \(p_{r}\)/m
The radial-force equation is obtained by taking the second derivative of r with respect to time and substituting Hamilton's equation of motion for pr.
d²r/dt² = 1/m dpr/dt
d²r/dt² = -1/m (δH/δr)
d²r/dt² = p²φ/m²r³ - 1/m dU/dr
d²r/dt² = L²/m²r³ + 1/mF(r)
No, it is not a constant of motion.
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1. Summarise Lamarck's theory of evolution: list 2 ideas proposed by Lamarck. (2)
2. Summarise Darwin's theory of evolution: list 2 ideas proposed by Darwin. (2)
3. Draw a diagram (this isn't art class, don't worry) of how an organism might evolve under Lamarck vs Darwin's theories of evolution. You can use an existing organism or make one up. (4)
Lamarck's theory of evolution, also known as Lamarckism, proposed two main ideas. Firstly, the theory of use and disuse suggests that organs or traits that are used more frequently become stronger and more developed, while those that are not used gradually deteriorate over generations. Secondly, the theory of inheritance of acquired characteristics states that an organism can pass on traits acquired during its lifetime to its offspring.
Under Lamarck's theory, an organism might evolve by developing or strengthening certain traits through use and passing them on to the next generation. For example, if a giraffe stretches its neck to reach leaves high in the trees, its offspring would inherit a longer neck. This gradual elongation of the neck would continue over generations.
In contrast, under Darwin's theory of natural selection, an organism might evolve through the process of adaptation to its environment. For instance, consider a bird population with varying beak sizes. If the available food source consists of small seeds, individuals with smaller beaks are more likely to survive and reproduce, passing on their genes for smaller beaks. Over time, the average beak size in the population would decrease due to the selective advantage of smaller beaks in obtaining food.
In summary, Lamarck's theory proposed that acquired traits can be inherited, leading to gradual changes in an organism's characteristics. Darwin's theory, on the other hand, emphasized the role of natural selection in the adaptation of organisms to their environment, resulting in the accumulation of advantageous traits over generations.
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Two people carry identical 40.0N boxes up the ramp. The ramp is 2.00m long and 1.00m high. Person A walks up the ramp in 2.00s. Person B walks up the ramp in 4.00s. What is the difference in power the two people use to carry the boxes up the ramp
The difference in power for two people carrying the boxes up the ramp is 30 W.
Given the following data:
W = 40.0 N is the weight of a box.
The ramp's length is L = 2.00 m.
The platform height is h = 1.0 m.
t = 2.0 s is the time interval for the first person.
t' = 4.0 s is the time interval for the other person.
Power is the rate at which energy is used. The expression for the Power is given in the given question as,
P = W×(L+h)/t
Assume that you are solving for the first person.
P₁ = W(L+h)/t₁.................................................................. (1)
Substitute the following values into equation (1):
P₁ = 40(2+1)/2
P₁ = 20(3) (3)
P₁ = 60 W.
Regarding the second person,
P₂ = W(L+h)/t₂..................................................................... (2)
Fill in the blanks in equation (2) as follows:
P₂ = 40(2+1)/4
P₂ = 10*(3) *3)
P₂ = 30 W
Obtaining the difference in power as
P = P₁ - P₂
P = 60-30
P = 30 W
As a result, we can conclude that the difference in power for two people carrying the boxes up the ramp is 30 W.
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What is related to the volume of a sound wave?
A. Amplitude
B. Frequency
C. Speed
D. Wavelength
Answer:
A. amplitude
Explanation:
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an electrically charged object can be used to attract:
An electrically charged object can be used to attract any object with an opposite charge.
This is due to the fundamental principle that opposites attract and repel in physics.
Electric charge is a fundamental property of matter that gives rise to electromagnetic interactions. An electric charge, whether positive or negative, produces an electric field that surrounds it. This field exerts a force on any other charge in its vicinity that is either attracted to or repelled from it. Electric charge is a fundamental property of matter that produces a variety of electric phenomena. When the charge is concentrated in a localized region of space, the object is electrically charged. When there is a net accumulation of charge in an object, it becomes electrically charged. An electrically charged object produces an electric field in its vicinity, which exerts a force on other charged objects. An electrically charged object can be used to attract objects with an opposite charge or repel objects with the same charge.
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What should be done when taking a voltage measurement of an unknown source?
The precautions and steps to be taken for voltage measurement of an unknown source are given below.
When taking a voltage measurement of an unknown source, the following steps should be taken:
Ensure that the instrument being used to measure the voltage is set to the appropriate range for the voltage being measured.Verify that the instrument is functioning properly by performing a self-test or calibration check, if available.Connect the instrument leads to the source being measured. The red lead should be connected to the positive side of the source and the black lead to the negative side.Check the polarity of the voltage source to ensure that the leads are connected correctly. If the polarity is reversed, the instrument will measure a negative voltage.Measure the voltage and record the value.Repeat the measurement several times to ensure that the readings are consistent and accurate.If the voltage being measured is AC, ensure that the instrument is set to AC voltage measurement mode.If the voltage being measured is DC, ensure that the instrument is set to DC voltage measurement mode.If the voltage being measured is high, use caution and proper safety procedures to avoid injury or damage to the instrument.Learn more about voltage;
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27. A force of 91 N is exerted straight up on a stone that has a mass of
0.75 kg. Calculate
a. the weight of the stone.
b. the net force acting on the stone.
c. the acceleration of the stone.
1) A low-power college radio station broadcasts 10 Wof electromagnetic waves.
At what distance from the antenna is the electric field amplitude 2.0×10−3V/m, the lower limit at which good reception is possible?
Express your answer to two significant figures and include the appropriate units.
2) A TMS (transcranial magnetic stimulation) device creates very rapidly changing magnetic fields. The field near a typical pulsed-field machine rises from0 T to 2.5 T in 200 μs. Suppose a technician holds his hand near the device so that the axis of his 2.1-cm-diameter wedding band is parallel to the field.
Part A
What emf is induced in the ring as the field changes?
Express your answer to two significant figures and include the appropriate units.
Part B
If the band is made of a gold alloy with resistivity 6.2×10−8Ω⋅m and has a cross-section area4.5 mm2 , what is the induced current?
Express your answer to two significant figures and include the appropriate units.
1.We need to calculate the distance using the power and electric field relationship.
2.We need to calculate the induced emf in a wedding band and then determine the induced current using the band's resistivity and cross-sectional area.
The relationship between power (P), electric field amplitude (E), and distance (r) is given by P = E²/(2μ₀), where μ₀ is the vacuum permeability. Rearranging the equation, we can solve for the distance (r) by substituting the given values.
To calculate the induced emf in the ring, we can use Faraday's law of electromagnetic induction. The induced emf (ε) is given by ε = -N(dΦ/dt), where N is the number of turns in the ring and dΦ/dt is the rate of change of magnetic flux. By substituting the given values, we can calculate the induced emf.
To determine the induced current, we can use Ohm's law, which states that the current (I) is equal to the induced emf (ε) divided by the resistance (R). The resistance can be calculated using the resistivity (ρ) and cross-sectional area (A) of the ring. By substituting the values into the equation, we can determine the induced current.
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Which of the following statements about density is true.
there is nothing there
A car is initially driving 20 m/s due East. The driver makes a left turn. After completing the turn, the car is moving 21 m/s due North. If this turn takes five seconds to complete, what is the magnitude of the average acceleration of the car during the turn
The magnitude of the average acceleration of the car during the turn is approximately 5.8 m/s².
To find the magnitude of the average acceleration of the car during the turn, we can use the formula for average acceleration:
Average acceleration (a_avg) = (Change in velocity) / (Change in time)
Given:
Initial velocity (v_i) = 20 m/s due East
Final velocity (v_f) = 21 m/s due North
Time taken (Δt) = 5 seconds
To calculate the change in velocity, we can use vector subtraction:
Change in velocity (Δv) = v_f - v_i
Since the velocities are in different directions, we need to consider their vector components. Let's break down the velocities into their x and y components:
v_i = 20 m/s due East
v_f = 21 m/s due North
The x-component of v_i is 20 m/s and the y-component is 0 m/s.
The x-component of v_f is 0 m/s and the y-component is 21 m/s.
Now, we can calculate the change in velocity:
Δv = (Δv_x, Δv_y) = (0 m/s - 20 m/s, 21 m/s - 0 m/s)
= (-20 m/s, 21 m/s)
The change in time (Δt) is given as 5 seconds.
To calculate the average acceleration:
a_avg = Δv / Δt
= (-20 m/s, 21 m/s) / 5 s
= (-4 m/s², 4.2 m/s²)
To find the magnitude of the average acceleration, we take the square root of the sum of the squares of the components:
|a_avg| = √((-4 m/s²)² + (4.2 m/s²)²)
≈ √(16 m²/s⁴ + 17.64 m²/s⁴)
≈ √(33.64 m²/s⁴)
≈ 5.8 m/s²
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The concept of inertia forms the basis for Newton's Third Law of Motion True False
Given
The concept of inertia forms the basis for Newton's Third Law of Motion
To find
The given statement is true or false
Explanation
The third law of motion states that every action has a equal and opposite reaction
Inertia is the property by virtue of which an object at rest tends to be at rest and object at motion tends to be at motion
Thus both the concept are not similar
Conclusion
The given statement is false
(PLEASE HELP !! )Does the chemical equation follow the Law of Conservation Of Matter?
A. No
B. Yes
Please explain to.
Answer: No
The Law of Conservation infers that the matter within a system will perserve its quantity (less there's an outside factor which disrupts the system). There should be more Cl within the products side of the equation, and more Br within the reactants side (there should be general adjustment to make this problem balanced), so that the matter is equal in quantity within both sides of the equation.