Equal but in opposing directions, forces of the car and the force of the bus.
Given that both objects are moving, you can be sure that the collision is elastic and that the forces involved in the collision between the bus and the car will be equal.
Without force, objects cannot be moved, stopped, or changed direction. Force can be defined as the pushing or pulling of any object as a result of the object's interaction or movement. In nature, there are various types of forces that interact quantitatively between two physical bodies, such as an object and its surroundings. If an object is in motion or in a static state, the position of the object can only be changed by an external force—referred to as force—pushing or pulling against it. The various types of contact force include spring force, applied force, air resistance force, normal force, tension force, friction force, and others that are generated when we exert some effort on an object. Non-contact forces, which include electromagnetic, gravitational, and nuclear forces, are another category of forces that exist at a distance.
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1) a solid sphere has a radius of 5 cm and a mass of 350 grams. what is its average density? a hollow sphere has the same radius and mass. what is its average density?
To calculate the average density of the hollow sphere learn the radius and density.
What is radius?
Simply halving the circle's diameter yields the radius formula. The radius of the ring is the line segment formed when we join a point on a circle's circumference to the exact center. The radius of a circle is the distance separating its center from its perimeter.
What is density?
When a material is packed tightly, it is said to have a high density. Its definition is the ratio of mass to volume. Density begins with the letter D. density formula is given as = m/V for objects with masses m and volumes V.
Volume of solid sphere = 4 pi r^3 / 3
= 4 x pi x 5^3 / 3
= 523.6 cm^3
mass = 350 g
average density = mass / volume
= 0.668 g/cm^3 Or 668 kg / m^3
If Sphere is hollow, then also it will acquire same volume in the space.
hence average velocity will not change.
Therefore, its average density is 0.668 g/cm^3 Or 668 kg / m^3
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Find the magnitude and vector direction of the sum of these two vectors:
Magnitude of the resultant vector is 20.03.
What is resultant vector?A resultant vector is described as a single vector that has the same consequence as several other vectors taken together. To create the resulting vector, two vectors facing the opposite direction are subtracted from one another. Here, the vector B is pointing in the opposite direction of the vector A, and the resulting vector is called R.
Resultant vector = [tex]\sqrt{A^2 + B^2 + 2AB cos\theta}[/tex]
Resultant vector = [tex]\sqrt{9.66^2 + 12^2 + 2(9.66)(12) cos45}[/tex]
Resultant vector = 20.03
Magnitude of the resultant vector is is 20.03.
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Mort and Velma are twins, born at the same time on Earth. Velma is taken on a long trip into outer space, at a speed close to light speed, and returns to Earth. When she returns,
a. Mort and Velma both observe that Velma is older than Mort.
b. Mort and Velma both observe that Mort is older than Velma.
c. Mort observes that he is older than Velma, and Velma observes that she is older than Mort.
d. Mort observes that he is younger than Velma, but Velma will observe that she is younger than Mort.
e. Mort and Velma observe that they have aged equally
Using the concepts of light, we got that option b)Mort and Velma both observe that Mort is older than Velma is observed by Velma who is taken on a long trip into outer space, at a speed close to light speed.
Light or visible light is the electromagnetic radiation that can be perceived by human eye. Visible light is usually defined as having wavelengths in range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz, between infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths).
In physics, the term "light" may actually refer more broadly to electromagnetic radiation of any wavelength, whether the visible or not.[4][5] In this sense, gamma rays, X-rays, microwaves and the radio waves are also light. The primary properties of light are the intensity, propagation direction, frequency or the wavelength spectrum and polarization.
Hence, Mort and Velma are twins, born at the same time on Earth, when Velma is taken on a long trip into outer space, at a speed close to light speed, and returns to Earth, and when she returns, Mort and Velma both observe that Mort is older than Velma.
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as light hits the retina, the first structure the light encounters is a rod or a cone. as light hits the retina, the first structure the light encounters is a rod or a cone. true false
As light hits the retina, the first structure the light encounters is a rod or a cone is a false statement.
What is Retina?The layers of light-sensitive nerve tissue at the back of the eye that take in images and transmit them as electric signals to the brain via the optic nerve is termed as retina.
What is light?Electromagnetic radiation that can be seen by the human eye is known as light or visible light. Typically, visible light is characterized as having wavelengths between 400 and 700 nanometers, or 750 and 420 terahertz, or frequencies between the infrared and the ultraviolet.
Contrary to what might make sense, light has to pass through the ganglion cells first, through the bipolar cells, and finally strikes the rods and the cones.
Hence, as light hits the retina, the first structure the light encounters is a rod or a cone is a false statement.
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place the elements in order from smallest to largest atomic number.
iron
sodium
uranium
neon
silicon
Answer: Neon,Sodium, Silicon, Iron and Uranium.
true or false: the vast size of our solar system makes it impossible for a large, civilization-threatening asteroid or comet to collide with earth.
The vast size of our solar system makes it impossible for a large, civilization-threatening asteroid or comet to collide with earth is the False statement.
What is an asteroid?Small, stony objects called asteroids orbit the Sun. Despite orbiting the Sun similarly to planets, asteroids are far smaller than planets. Small, stony objects called asteroids orbit the sun.
What is a comet?Large ice and dust-based bodies known as comets orbiting the Sun. Most recognisable for their lengthy, streaming tails.
Comet or large, civilization-threatening asteroid has nothing to do with the vastness of solar system in effecting the earth from damage to the human race or to destroy it completely.
Civilization-threatening asteroid or comet large enough to do serious damage to the human race will eventually collide with Earth even if the solar system is very vast.
Hence, the vast size of our solar system makes it impossible for a large, civilization-threatening asteroid or comet to collide with earth is the False statement.
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What is the relative age of the crater copernicus?
The relative age of the crater Copernicus is 800 million years.
Crater is nothing but a large bowl-shaped cavity in the ground or on a celestial object, typically one caused by an explosion or the impact of a meteorite.
Copernicus is a lunar impact crater located in eastern Oceanus Procellarum. It was named after the astronomer Nicolaus Copernicus. It typifies craters that formed during the Copernican period in that it has a prominent ray system. It one of the most prominent craters on the Moon. It constitutes a classic example of a relatively young, well-preserved lunar impact crater.
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Test
Consider two planets that have the same mass but are very different in size. Which statement describes the gravitational pull
that an object would experience on the surface on each planet? (1 point)
O The object would experience a much greater gravitational pull on the larger planet.
O The object would experience the same gravitational pull on each planet.
O The object would experience only a slightly greater gravitational pull on the larger planet.
O The object would experience a greater gravitational pull on the smaller planet.
When an object is placed on the surface of two planets that have the same mass but are very different in size, then the the object would experience a greater gravitational pull on the smaller planet.
What is the weight of an object and what is acceleration due to gravity?
Weight of an object:
The force exerted by gravity on a body or an object is known as weight.The formula provides the weight of an object mathematically;W = mg
Where;
The object's mass is m.
Gravitational acceleration, or g, is measured.
Acceleration due to gravity, g:
The acceleration that objects experience due to the combined action of gravity and centrifugal force is known as the Earth's gravity, or g, and it is represented by the Greek letter g.The formula for calculating gravitational acceleration is g = GM/r2.The square of the distance from the planet's core and the acceleration caused by gravity, or g, are inversely proportional. Likewise, if there were two planets with the same mass but different sizes. Take into account the fact that planet A's radius is smaller than planet B's radius. This implies that the planet A's g will be higher than the planet B's g. Since the object's mass is constant, the weight of the object on planet A will be higher than the weight of the object on planet B.
Hence, The object would experience a greater gravitational pull on the smaller planet.
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A plane travels a distance of 5. 0×102 m north while being accelerated uniformly from rest at the rate of 5. 0 m/s2. What final velocity does it attain?.
The final velocity it attains is 70.7 m/s
Velocity is the directional velocity of an object in movement as a demonstration of its price of exchange in function as found from a specific body of reference and as measured by using a specific well-known time.
Speed is the time fee at which an item is shifting along a direction, at the same time as velocity is the rate and route of an object's movement. placed any other way, speed is a scalar cost, whilst pace is a vector.
Speed is the velocity at which something moves in a selected course. for example, the velocity of a car traveling north on a highway, or the velocity at which a rocket travels after launching. In the scalar manner, the absolute price value of the rate vector is continually the velocity of the motion.
Calculation:-
v² = U² + 2aS
V² = 0 + 2×5×500
V² = 5000
V = 70.7 m/s
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a circularly-polarized antenna is designed to receive a rhcp wave traveling in the z direction. it consists of two wire antennas, one oriented in the x direction and one oriented in the y direction. the signals are combined from each antenna with a 90o phase shift between the two antennas, so that the total open-circuit voltage that is received is
The total open-circuit voltage that is received is 19.41V.
Solution:
RCHP traveling in the z-direction
E = E₁₀ cos(wt - βz) + Ey₀ sin(wt - βz)
E = [tex]\sqrt{E_{y0}^{2} + E^{2} y_{0}[/tex] = [tex]\sqrt{E^{2}_{O} } +E^{2}_{O}[/tex] = [tex]\sqrt{2} .Eo[/tex]
= [tex]\sqrt{2} Eo = 19.41 = Eo = 19.41[/tex]
Open circuit voltage is the voltage difference measured between two terminals when no current is being drawn or supplied. Short-circuit current is the current that flows when the voltage difference between terminals is forced to zero. No current flows in the circuit, but there is a voltage drop between the two points.
As a result, in an open circuit, the current through it is zero but the voltage is present. The current becomes zero and the power equals VI. When an open circuit is introduced, current flow through the circuit is interrupted. The voltage drop across each resistive element is zero when no current is flowing. However, the source potential difference appears to be open.
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What new rock formations did you see when the landscape was only exposed to energy from the sun?.
The rock formations that are visible when the landscape is exposed to energy from the sun are sedimentary rocks.
A landscape is a geomorphological unit that is categorized based on characteristics such as elevation, slope, orientation, stratification, rock exposure, and soil type.
Sedimentary rock or also known as sedimentary rock is a rock that forms on the surface of the earth under conditions of low temperature and pressure. These rocks originate from rocks that were formed earlier, which experience weathering, and erosion, and then weathering is transported by water, air, or ice, which are then deposited and accumulate in depositional basins, forming sediments. These sedimentary materials then compact, harden, undergo lithification, and form sedimentary rocks.
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the magnetic field strength at the north pole of a 2.0- cm -diameter, 8- cm -long alnico magnet is 0.10 t . to produce the same field with a solenoid of the same size, carrying a current of 2.0 a , how many turns of wire would you need?
Magnetic field - You would need N = 3032 of wire.
What is a magnetic field?
The magnetic influence on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is traveling through a magnetic field.
As seen in the following equation, a solenoid's magnetic field is
B = μ₀ n I
where n is the turn density, I is current and has a permittivity in a vacuum of 4 107 N/A2.
Let's use this equation to solve the issue; in this case, the length of the magnet is the unit of length, and the turn density is the number of turns per unit length.
L = 8 cm = 0.08 m
Let's compute.
B = μ₀ N/L I
N = B L / μ₀ I
N = 0.10 0.08 / (4π 10⁻⁷ 2.1)
3,032 103 turns,
Hence, the number of turns is 3032.
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Suppose that you are holding a pencil balanced on its point. If you release the pencil and it begins to fall, what will be the angular acceleration when it has an angle of 10. 0 degrees from the vertical? a typical pencil has an average length of 15. 0 cm and an average mass of 10. 0 g. Assume the tip of the pencil does not slip as it falls.
If the pencil falls from a perfectly vertical position while maintaining its angular acceleration, the time it takes for it to hit the ground is 0.4299s.
How to calculate the time taken?The passing time is calculated by dividing the distance by the speed. To find the distance, multiply the speed by the passage of time. The simplified form of these equations is s=d/t, where s stands for speed, d for distance, and t for time.
[Time = Distance Speed] is the formula for calculating time. Utilizing the formula [Distance = Speed Time], one can determine the distance.
The angular acceleration will be determined using Newton's second angular law. As follows:
τ = I α
ωr = I α
Here, the pencil's center is where the weight is placed, ,
sin 10 = r / (L/2)
Maker is the subject of the formula
r = L/2 sin 10
The moment of inertia at that point will be:
I = 1/3 M L²
(1/3 m L2) = mg L / 2 sin 10
αf = 3/2g/Lsin 10
α = [3/2 × 9.8] / [0.150 sin10]
α = 17 rad/s²
The moment of inertia is then: The angle between the vertical and the ground is then:
θ = π / 2
t = √(2 π/2 α )
t = √(π / α )
t = √(π / 17)
t = √3.142 / 17
t = √0.1848
t = 0.4299s
The angle from the vertical to the ground will then be denoted as: As a result, the time it takes for the pencil to touch the ground is 0.4299 seconds.
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how many tightly bound molecules could a single ray of frequency 2.77 x 1020 hz break apart? the binding energy of such a molecule is 10 ev. your answer should be a number with two decimal places in the form: n x 105, indicate only n.
Answer:
E = h ν
E = 6.63E-34 * 2.77E20 = 1.84E-13 energy of incident beam
1 eV = 1.60E-19 10 eV = 1.60E-18 Joules
n = 1.84E-13 / 1.60E-18 = 1.15E5
n = 1.15
Which term found in the electromagnetic spectrum is determined by its wavelength?.
Color is the term found in the electromagnetic spectrum is determined by its wavelength.
Radio waves, gamma-rays, visible light, and all the other elements of the electromagnetic spectrum are electromagnetic radiation. Electromagnetic radiation can be defined in phrases of a movement of mass-much less particles, called photons, each visiting in a wave-like pattern at the velocity of light.
Wavelength is the space from one point on a wave to the same point on the subsequent wave. Frequency is the range of waves that skip through a factor in a 2d. Chemistry Interaction of light with count number.
The wavelength of light is an essential property for it's miles this that determines the character of the light. pink light has a distinctive wavelength to that of blue mild and green mild has a specific wavelength from each of them.
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below are six different sequences of snapshots taken as the two pulses meet in the middle of the string. time increases from top to bottom in each sequence. which sequence correctly represents the displacement of the string as the pulses interfere?
Option C is the sequence which correctly represents the displacement of the string as the pulses interfere. When a wave pulse encounters a free end then it reflects the same way as incident path which is depicted in option C.
Longitudinal waves are waves in which the medium is moved in the same direction as the wave's propagation. The wavelength determines the separation between the centres of two adjacent compression or rarefaction areas.
An object's position changes if it moves in relation to a reference frame, such as when a passenger moves to the back of an aeroplane or a lecturer moves to the right in relation to a whiteboard. Displacement describes this shift in location.
The amount of medication needed to replace 1 gramme of suppository base is known as the displacement value. Coca Butter or Theobroma oil is the most used foundation for suppository preparation. Suppositories are traditionally made in suppositories moulds, which typically accommodate 1 or 2 grammes of base.
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The reason that most seti programs choose to listen at microwave radio frequencies is that.
Microwaves are most energy efficient way to send information.
What are SETI programs?Electromagnetic waves are a general term for familiar light and radio waves, but they also include gamma rays, X-rays, ultraviolet rays, and infrared rays. All of these forms of electromagnetic radiation or waves travel at the speed of light, the highest possible speed. The only difference between these types of electromagnetic waves is their length, or wave, or "wavelength." Another way to characterize waves is the number of waves received per second, since they all travel at the speed of light. This is the wave frequency. A specific range of radio frequencies from 1 GHz to 10 GHz, "microwaves", is particularly well suited for interstellar communications. At lower frequencies, our galaxy emits enormous amounts of radio waves, creating a large amount of background noise. At higher frequencies, the Earth's atmosphere, and possibly other Earth-like planets, absorb and emit a wide range of radio frequencies. The result is a quiet "microwave window" that enables efficient wireless communication.
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a bullet with a mass of 25 grams is traveling at a speed of 250 m/s. the bullet encounters a 35-kg wooden block at rest and upon impact, gets embedded within the block. what is the velocity with which the objects move together after the collision?
The velocity with which the objects move together after the collision is 5.604 m/s
State the the law of momentum conservation.
The following is an explanation of the law of momentum conservation.
The total momentum of the two objects prior to the collision is equal to the total momentum of the two following the collision for an impact between object 1 and object 2 in an isolated system. In other words, the momentum obtained by the object 2 equals the momentum missed by object 1.The bullet and the block have the same speed after colliding, therefore we utilize momentum conservation and account for that.
mv1_i + Mv2_i = mv1_f + Mv2_f
Given values from the question,
Mass of bullet = m =25 g = 0.025 kg
Mass of wooden block = M = 35 kg
Initial speed of bullet = v1_i = 250 m/s
Putting the values in the momentum conservation equation,
mv1_i + 0 = (m + M) V
0.025 x 250 = (0.025 + 35) V
V = 35.025 / 6.25
= 5.604 m/s
Hence, the velocity with which the objects move together after the collision is 5.604 m/s
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Enzo is developing a model of the electron transport chain. What is the role of atp and nadh in the model?.
The role of ATP and NADH in the model is that the ATP is used to synthesize NADH in one step of the chain.
What is meant by ATP?ATP is an organic substance that supplies energy to several functions in living cells, including muscular contraction, nerve signal propagation, condensate dissolving, and chemical synthesis. ATP is the molecular unit of currency of intracellular energy transfer and is found in all known forms of life. When it is utilized in metabolic processes, it either changes to adenosine diphosphate (ADP) or adenosine monophosphate (AMP) (AMP). Other processes recycle ATP. Every day, the human body recycles its own body weight equal in ATP. It is also a coenzyme and a precursor of DNA and RNA. So, ATP is used to synthesize NADH in one step of the chain.
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at what altitude should a satellite be placed into circular orbit so that its orbital period is 48 hours?
In order for the satellite to have an orbit with a 48-hour period, its orbit must be positioned in a circular orbit at an altitude of 60.689*106m. At this time, altitude is calculated from Earth's surface.
Therefore, the radius of the Earth is subtracted from the total radial distance to get the altitude of the satellite's orbit. orbit of a satellite Satellite orbits are divided into high and low orbits, polar orbits (when the earth's spin axis is included within the orbit plane), equatorial orbits (when the earth's equatorial plane coincides with the orbit plane), and pro-grade and retrograde or bits (the direction of satellite motion is either eastward or westward).
R = 67.067*10^6 m
As a result, height (h) is equal to total radial distance (r) minus earth's radius (R). For example, h=(60.067 - 6.378)*106m; h= 60.689*106m.
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an electron-volt (ev) is the amount of energy needed to move a single electron from an electric potential of 0 to an electric potential of -1 v. the charge of an electron is approximately -1.602 x10-19 c. how many joules is an electron volt?
The joules carrier by an electron volt will be = 1.602 x 10-19 J
What do you mean by electric potential?
Electric potential can be defined as the amount of work which is needed to move an unit charge from a reference point to a specific point against an electric field.
It can be calculated by the given formula
V=kQ/r or V = k Q / r . It is a scalar quantity while the electric field is a vector.
Uses of Electric Potential.
Potential energy a test charge would have at a given location due to a source charge.An incandescent light bulb that is turned off. To measure light and heat energy.Hence, in the above question the joules carrier by an electron volt will be = 1.602 x 10-19 J.
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the resistance of a drill is ___ ohms where the nameplate supplies the following information: 5.4 amps 120 volts
Answer: 648 Ohms
Explanation:
RA = VI
Resistance = voltage x current
R = 120V x 5.4 = 648 Ohms
now the switch is closed, and you wait for a long time. how much electric charge does the capacitor store now?
The electric charge the capacitor store now is 0.065 C.
What is a capacitor?
A capacitor is a device that uses the accumulation of electric charges on two nearby surfaces that are electrically isolated from one another to store electrical energy in an electric field. It has two terminals and is a passive electrical component. referrer=search Results refers to a capacitor's effect. Initially when switch S is open for a long time the charge stored on the capacitor is given by the following equation.
The solution to this question is too large so I am adding this screenshot kindly check the attachment:
Now final charge on the capacitor after closing the switch for a long time
Q = CE
Q = 3.65*10^{-3}*17.76= 0.065 C
Hence, the electric charge the capacitor store now is 0.065 C.
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nichrome wire 85 cm long and 0.25 mm in diameter is connected to a 1.6 volt flashlight battery. what is the electric field inside the wire?1.88 correct: your answer is correct. v/m
The electric field will be 1.9 V /m
The length of the wire is l = 85.
The diameter of the wire is d = 0.25mm
.The voltage of the battery is V = 1.6 V.
(a) The expression for the electric field inside the wire is,
E=( V / L )
Substituting the given values in the above expression, we will get
E = 1.6V / 85cm ( 1m /100cm)
= 1.6V / 0.85 m
= 1.88 V / m
= 1.9 V / m
Hence, the electric field will be 1.9 V /m.
What do you mean by Electric Field ?
Electric field can be defined as an electric property which is associated with each point in the space where a charge is present in any form. An electric field is also described as the electric force per unit charge.
The formula of electric field is given as;
E = F /Q
Where,
E is the electric field.
F is a force.
Q is the charge.
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.
an object is at rest on the ground. the object experiences a downward gravitational force from earth. which of the following predictions is correct about why the object does not accelerate downward? select two answers. justify your selections.
Predictions about why the object does not accelerate downward are (1) the bonded molecules of the object are repelled upward by the bonded molecules of the ground with the same magnitude as the gravitational force downward on the object, and (2) the normal force is exerted upward on the object from the ground with the same magnitude as the gravitational force downward on the object.
What is the normal force?The normal force is simply the force that two surfaces in contact exert to each other to prevent themselves from passing through each other. Since the normal force is a contact force, two surfaces that aren't in contact can't exert a normal force on each other. The normal force will be as large as necessary to make net force equal zero.
The normal force is generated by the electromagnetic force: the electrons in an object are pushing against the electrons in another object.
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7) someone suggests that astronomers build a special gamma-ray detector to detect gamma rays produced during the proton-proton chain in the core of the sun, just like they built a neutrino detector. explain why this would be a fruitless effort.
Through the act of counting and calculating the energy of single photons emitted from elements, gamma ray detectors calculate electromagnetic radiation.
Gamma-ray detection is carried out photon-by-photon, just as X-ray detection. By observing the impact they have on materials, gamma rays can be found. A gamma ray can drive an electron to a higher level or collide with it and cause it to scatter like a pool cue (Compton scatter) (photoelectric ionization).
Protons are transformed into neutrons, positrons, and electron neutrinos as part of the proton-proton chain, which generates a significant amount of energy. The primary reaction in the majority of main-sequence stars, including the Sun, is the proton-proton chain. A nuclear fusion reaction, the proton-proton chain releases energy as the energy in the nuclear bonds diminishes. To counteract the protons' natural tendency to resist one another, smaller nuclei must have more energy.
An atom of the unstable isotope germanium-71 can be created when a neutrino interacts with a gallium-71 atom. The germanium was then concentrated and removed chemically. As a result, neutrinos were discovered by monitoring germanium's radioactive decay.
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Consider a person of weight w standing in an elevator that is accelerating downward. An upward force n is exerted by the elevator floor on the person. The relationship between n and w is.
W-weighted person standing in an escalator that is descending quickly. The person is subjected to an upward force of N from the elevator floor. (Reply N=W.)
What does an elevator do?A vehicle that travels in a mine shaft to transport people or cargo between floors of a multi - storey building is an elevator, also known as a lift. The majority of contemporary elevators are moved by electric motors through a network of cables & sheaves with the help of a counterweight (pulleys).
What makes it an elevator?The word "elevator" is really the name of the a lift manufactured by a firm in the US. People began to refer to elevators as elevators since the company was just so successful and put them in so many locations.
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#SPJ4Which statement best describes a weak base?(1 point)
a.) It donates protons and only partially dissociates in water.
b.) It accepts protons and only partially dissociates in water.
c.) it donates protons and completely dissociates in water.
d.) It accepts protons and completely dissociates in water.
Answer:
It accepts protons and only partially dissociates in water.
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a grinding wheel is rotating with an angular velocity of 251 radians per second, find the period of one revolution.
Using the concepts of angular velocity, we got that 0.025sec is the period of one revolution for a grinding wheel which is rotating with an angular velocity of 251 radians per second.
We know that angular velocity is defined as the change of angular displacement with respect to time.
or ,ω=θ/t
Here, grinding wheel is circular in shape means total angular displacement is 360 degree or 2[tex]\pi[/tex]
So according to the formula,
=>251=2π/t
=>t=2π/251
=>t=(2×3.14)/251
=>t=6.28/251
=>t=0.025sec
Hence, if a grinding wheel is rotating with an angular velocity of 251 radians per second, the period of one revolution is 0.025sec.
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a man falls 2.0 m to the floor (assume down to be negative)
how long does the fall take?
what is his velocity when he hits the floor?
Answer:
Approximately [tex]0.64\; {\rm s}[/tex].
Velocity: approximately [tex]6.3\; {\rm m\cdot s^{-1}}[/tex].
(Assuming that air resistance is negligible, and that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] assuming that the fall started from rest.)
Explanation:
If air resistance is negligible, acceleration will be constantly [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex] during the fall.
Let [tex]x[/tex] denote the displacement. In this question, [tex]x = (-2.0)\; {\rm m}[/tex]. Note that [tex]x[/tex] is negative since the position after the fall is below the initial position.
The initial velocity at the beginning of the fall is [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex] under the assumptions.
Let [tex]v[/tex] denote the final velocity right before landing. Apply the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] to find [tex]v\![/tex]. Rearrange this equation to obtain:
[tex]\begin{aligned}v &= \sqrt{2\, a\, x + u^{2}} \end{aligned}[/tex].
Substitute in [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex], [tex]x = (-2.0)\; {\rm m}[/tex], and [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex] and solve for [tex]v[/tex]
[tex]\begin{aligned}v &= -\sqrt{2\, a\, x + u^{2}} \\ &= -\sqrt{2 \,((-9.81)\; {\rm m\cdot s^{-2}}) \, ((-2.0)\; {\rm m}) + (0\; {\rm m\cdot s^{-1}})^{2}} \\ &= \left(-\sqrt{2 \, (-9.81)\, (-2.0)}\right)\; {\rm m\cdot s^{-1}} \\ &\approx (-6.26)\; {\rm m\cdot s^{-1}} \\ &\approx (-6.3)\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
(Negative since the final velocity points downwards to the ground.)
In other words, the velocity right before landing would be approximately [tex](-6.3)\; {\rm m\cdot s^{-1}}[/tex].
The change in velocity during the fall would be:
[tex]\begin{aligned}v - u &\approx (-6.26)\; {\rm m\cdot s^{-1}} - (0\; {\rm m\cdot s^{-1}}) = (-6.26)\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Divide the change in velocity by acceleration to find the duration [tex]t[/tex] of the fall:
[tex]\begin{aligned}t &= \frac{v - u}{a} \\ &\approx \frac{(-6.26)\; {\rm m\cdot s^{-1}}}{(-9.81)\; {\rm m\cdot s^{-2}}} \\ &\approx 0.64\; {\rm s}\end{aligned}[/tex].