Answer: 1. throw or drop (something) from an aircraft or ship
2.to ensure mission success just in case the first one fails.
Explanation:
when a traffic accident is investigated, it is common for the length of the skid marks to be measured. how could this information be used to estimate the initial speed of the vehicle that left the skid marks?
This information could be used in the following ways: the braking distance of a skidding car will depend on its initial speed and the coefficient of kinetic friction.
Thus, if the coefficient of friction is known the initial speed can be determined from the length of the skid marks.
What do you mean by Initial speed?
Initial speed can be described as how fast an object travels when gravity first applies force on the object. It can be represented in the form of (u) and is generally measured in metres per second (m/s).
It can be represented in three ways.
v2=u2+2as v=u+ats=ut+0.5at2Through these formulas we can calculate the initial speed of any object. It helps in understanding various velocities, time principles.
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A 210 W heater is placed in 2kg of water and switched on for 200 seconds.
A: How much energy does the heater supply
B: Assuming that no thermal energy is lost, what is the temperature rise of water?
A. The amount of heat energy the heater supply is 42000 J
B. The temperature rise of the water is 5 °C
A. How do I determine the energy supplied by the heater?
We can determine the heat energy supplied by the heater as illustrated below:
Power (P) = 210 WattsTime (t) = 200 secondsEnergy (E) = ?Electrical power = Electrical eneryg / time
210 = Energy / 200
Cross multiply
Energy = 210 × 200
Energy = 42000 J
Thus, the energy supplied is 42000 J
B. How do I determine the temperature rise?
The temperature rise of the water can be obtained as follow:
Heat supplied (Q) = 42000 JMass of water (M) = 2 KgSpecific heat capacity of water (C) = 4184 J/KgºC Temperature rise (ΔT) =?Q = MCΔT
42000 = 2 × 4184 × ΔT
42000 = 8368 × ΔT
Divide both sides by 8368
ΔT = 42000 / 8368
ΔT = 5 °C
Thus, the temperature rise is 5 °C
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g consider a wire 2 ft long cut into two pieces. one piece forms a circle with radius r and the other forms a square with side length x. (a) determine a formula for the radius r in terms of x .
The radius in terms of x is 2/(π+4)
What is area?Area, a quantity that describes the extent of an area on a plane or curved surface. The area of a planar region refers to the area of a shape or planar layer, while surface area refers to the area of an open surface or boundary of a three-dimensional object.
Given that,
y forms a circle of radius r
y = 2πr
r = y/2π
(2-y) forms Square Side x
(2-y) = 4x
x = (2-y)/4
Now Sum of Areas = Area of Square + Area of Circle
Sum = πr² + x²
Substitute the values of r and x in above equation:
A(y) = y²/4π + (y-2)²/ 16
To maximize Area A(y)
A'(y) = 0
2y/4π + 2(y-2)/16 = 0
y/2π + (y-2)/8 =0
y = 2π/(π+4)
For maximum sum of areas,
x = 2/π + 4
Hence, The formula for the radius r in terms of x and for the maximum areas is x=2/(π+4)
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If you pour hot soup into a bowl, and the bowl stays cool to the touch, you can assume that
A
the bowl is a good insulator of heat.
B
the bowl is a good conductor of heat.
C
the bowl’s temperature cannot be measured.
D
the bowl transfers most of its heat through radiation.
Answer:
A
Explanation:
since it did not absorb the heat then it is an insulator
Which form of electromagnetic radiation has photons with the highest energy? Group of answer choices Infrared Radiation Gamma Rays Microwaves Radio Waves X-rays
Gamma rays is a form of electromagnetic radiation that has photons with the highest energy.
Gamma rays are a form of electromagnetic radiation (EMR). They are the similar to X-rays, distinguished only by the fact that they are emitted from an excited nucleus.
The energy of the photon is directly proportional to the frequency, that is Ε α υ. It means that if the photon has high frequency, then the energy of that photon will be high, and if the photon has lower frequency then the energy that the photon will be less.
Here it is given to determine the radiation that has high energy, which in turn means that radiation with the highest frequency is needed to be found. Hence, from the data of electromagnetic spectrum, the radiation with the highest frequency is the gamma rays with frequencies up to 10^19 Hz.
As gamma rays have the highest frequency, gamma rays will also have the highest energy, with energy extending up to few trillion electron volts.
Hence, the radiation with the highest energy is gamma rays.
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A patient with end-stage heart disease asks, "after i meet the physical criteria for a heart transplantation, will i then be selected as a candidate?" which response from the nurse is the most appropriate?.
Patients ought to meet physical and psychological standards to make sure that they may be candidates for coronary heart transplantation.
The Recipient affected person has to be referred to the transplant center with an irreversible and in any other case fatal disease ensuing in organ failure, whilst still being otherwise wholesome enough to live to tell the tale and gain from an organ transplant and to comply with a lifestyles-long medication routine.
Physical criteria indications for transplant in continual heart failure include sufferers who've disabling signs regardless of most fulfilling medical control or refractory arrhythmias no matter scientific and electrophysiological methods.
The doctor will make an incision on your chest. Your health care professional will separate your chest bone and open your rib cage in order that he or she will perform for your coronary heart. Your medical professional then removes the diseased heart and sews the donor heart into place. she or he then attaches the important blood vessels to the donor's coronary heart.
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With our current techniques, astronomers can typically only measure the minimum mass of a planet orbiting another star. To know the precise mass of the planet, they must also be able to determine.
To know the exact mass of a planet, we also need to be able to determine the angle at which the planet's orbit is tilted toward us.
How do you calculate the minimum mass of a planet orbiting another star?To determine the mass of a planet, astronomers usually measure the small motions of the star caused by the gravitational pull of the orbiting planet. For a planet, figuring out the mass of the Earth is an extraordinary challenge with current technology.
Therefore, to measure the mass of a planet, measure the period and orbital radius of all satellites orbiting the planet, plot graph against R³/T² for all satellites, and calculate the mass of the planet. This is one way to do that.
According to Kepler's laws: If the orbital size (a) is expressed in astronomical units (1 AU is the average distance between the Earth and the Sun) and the period (P) is measured in years, Kepler's third law states that his P² = a³ increase. where P is the Earth year, a is the AU, and M is the mass of the central body in units of the mass of the Sun.
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a car with a mass of 1000-liogram accerlerates from rest, and travels a distanceof 48 meters druing its first 4.0 seconds of uniform acceleration. what is its velocity at this points?
24 m/s will be the velocity at this point .
What is velocity?
Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). For example, "5 meters/second" is a scalar, but "5 meters/second east" is a vector. An object is said to be accelerating if its velocity, direction, or both change.
when v= u + at and v2-u2=2as , where u=0 ,t=4 , S = 48 m , manipulate the data and fine the answer.
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1. If I drop a watermelon from the top of one of the tower dorms at JMU, and it takes
3.50 seconds to hit the ground, how tall the building is in meters.
What is the acceleration of the watermelon as it falls?
Answer:
Below
Explanation:
The accelerateinon, a, of the watermelon is just the acceleration of gravity on Earth = 9.81 m/s^2
the height will be found by
Height = 1/2 a t^2 = 1/2 (9.81)(3.50)^2 = 60.1 m
suppose three planets all have similar rocky surfaces but different average densities as in the choices below. which planet is likely to have a large iron core? a)6000 kg/m3
b)3000 kg/m3
c)4500 kg/m3
The planet that is likely to have a large iron core if all three planets have similar rocky surfaces but different average densities is 6000 kg / m³
Density is directly proportional to he size of iron core. Larger the density of the planet larger will be the size of iron core of the planet. Smaller the density of the planet smaller will be the size of iron core of the planet.
Average density of a planet is the value of total mass divided by the total volume. If the average density of a planet is higher than 3000 kg / m³, the planet is terrestrial. If the average density of a planet is lesser than 2000 kg / m³, the planet is Jovian.
Therefore, the planet that is likely to have a large iron core if the planet with 6000 kg / m³
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You charge your cell phone every night while you are sleeping.
Throughout the school day you see your cell phone battery slowly decline. By
lunchtime your cell phone is almost dead. You remember in science class your
teacher saying that energy can't be created or destroyed. If the energy in your cell
phone battery wasn't destroyed, where did it go? Explain your answer,
Answer:Simple, it gets used up by the phone.
Explanation:Your phone uses the energy stored in the battery to perform the functions it does. Chemical energy gets converted to light (display), sound (speakers), electrical (internal processing of the phone), thermal (phone getting heated up), and to other forms.
an athlete swings a ball, connected to the end of a chain, in a horizontal circle. the athlete is able to rotate the ball at the rate of 7.80 rev/s when the length of the chain is 0.600 m. when he increases the length to 0.900 m, he is able to rotate the ball only 5.99 rev/s.
1276.9 m/s² is the angular acceleration of 0.900 m, he is able to rotate the ball only 5.99 rev/s.
v=33.9m/s
r=0.9 m
a=v²/r
a=1149.21/0.9
a=1276.9 m/s²
The rate at which the angular velocity in a circular motion varies over time is known as the angular acceleration. Rotational acceleration is another name for it. Given that it has both a magnitude and a direction, it is a vector quantity. Angular acceleration is represented by the letter alpha.
Variable velocity is what causes the acceleration. The phrase "angular acceleration" is used to describe variations in rotational speed in spinning objects. According to the connection, the angular displacement of a spinning object depends on time t. Every time a body rotates, it experiences angular acceleration. A quantitative vector can be used to express the change in angular velocity per unit of time.
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which of the following best describes this collision? view available hint(s)for part a which of the following best describes this collision? perfectly elastic partially inelastic perfectly inelastic
The best description of inelastic and elastic collisions is perfectly inelastic.
What are inelastic and elastic collisions?Collisions occur when one object strikes аnother. There аre two types of collisions:
Inelаstic collisions: momentum is conserved,Elаstic collisions: momentum is conserved аnd kinetic energy is conserved.Your question is incomplete, but most probably your question was
An inelastic collision is a collision in which kinetic energy is not conserved. In a partially inelastic collision, kinetic energy is lost, but the objects colliding do not stick together. From this information, you can infer what completely inelastic and elastic collisions are.
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a
b
с
3
A brick is shown in Figure 1.9. It has a mass of
2.8 kg.
65 mm
102.5 mm
215 mm
Figure 1.9: A brick labelled with its dimensions.
Give the dimensions of the brick in metres.
Calculate the volume of the brick.
Calculate the density of the brick.
Answer: A 0.065 METER 0.1025 METER 0.215 METER
B 0.001432 meter^3
C 1955.307 kg/m^3
Explanation:
[14] if you are going to measure current in a circuit, and that desired current passes through an existing resistor in the circuit, what method would you choose? b. [15] if you are going to measure current in a circuit, and that desired current does not pass through an existing resistor in the circuit, what method would you choose?
(a) If am going to measure the current and that desired current passes through I will an existing resistor to find the current using ohm's Law.
V= IR
Using the ohms Law another variable we can find is let Lenovo. To find Current any variable with two
The voltage & resistance.
So, I = V R
R is to be known.
If V= 1.5V, Then T= 1-5 100 = 0.015 Ampere
R = 100-2
But this is theoretical as the wire the load and even the supply have internal resistance. we Considering Also there are superconductors with zero resistance due to their properties in negative temperatures.
b) measure the current and the desired current doe as to not pass through the existing resistor,
Theoretically, if there is no resistance then it is a short Circu and the current will be infinite But Practically wires have resistance and simply I will find the Kurrent value by breaking the with and connecting the circuit.
We measure the current using a so-called ammeter. Some types of ammeters have a pointer on the dial but most have a digital display. Ammeters must be connected in series to measure the current flowing through the components in the circuit. There are two ways to measure current. One is based on electromagnetism and is associated with the early moving coil meter. The other is based on Ohm's Law, the main theory of electricity.
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consider two satellites s1 and s2 in circular orbits with periods of 8 hours and 16 hours how high are the satellites above the earth's surface?
Consider two satellites s1 and s2 in circular orbits with periods of 8 hours and 16 hours . satellites will be 80129 m and 130829 m high above the earth's surface
h1 = [tex]{(GM(e) * T^{2} / 4 pi^{2} )}^{1/3}[/tex] - R(e)
= ( 6.67 * [tex]10^{-11}[/tex] * 5.97 * [tex]10^{24}[/tex] * [tex]8^{2}[/tex] / 4 * [tex]3.14^{2}[/tex]) - 6371
= 80129 m
h2 = (6.67 * [tex]10^{-11}[/tex] * 5.97 * [tex]10^{24}[/tex] * [tex]16^{2}[/tex] / 4 * [tex]3.14^{2}[/tex]) - 6371
= 130829 m
satellites will be 80129 m and 130829 m high above the earth's surface
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A balloon tied up with a wooden piece is moving upward with velocity of 15 m/s. At a height of 300 m above the ground, the wooden piece is detached from the balloon. How much time will it take to reach the ground?
Time will it take to reach the ground is 9.3second
What is acceleration?
The velocity of an object may change due to an increase or reduction in speed or a change in direction of motion. The fall of an apple, the moon orbiting the earth, or a car stopped at a traffic light are all examples of acceleration. We can see from these examples that acceleration occurs when the direction of a moving object changes or its speed increases or decreases.
Acceleration is a vector quantity defined as the rate at which an object's velocity varies. If an object's velocity changes, it is accelerating.
If a person is moving quickly, sports announcers will occasionally state that he or she is accelerating. However, acceleration has nothing to do with speed. A person can be travelling very quickly yet not accelerating. Acceleration is the process of modifying the rate at which an object moves. If an object's velocity does not change, it is not accelerating. The data on the right indicate an accelerating object travelling northward. The velocity of the object changes throughout time.
We are using second equation of motion
s= ut+1/2[tex]t^{2}[/tex]
300=-15T +1/2*(10)[tex]T^{2}[/tex]
t = 9.3 second
Time will it take to reach the ground is 9.3second
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Why are the inner planets (those which orbit inside the asteroid belt) all relatively small and rocky, whereas the outer planets are large and mostly composed of gas?
Answer:
The temperature of the early solar system explains why the inner planets are rocky and the outer ones are gaseous.
Explanation:
The outer planets are much larger than the inner planets. Because of their large mass and cooler temperature, they have a very different composition; they are mostly made of light elements with extended atmospheres in a gaseous form. Outer planets exist in much bigger systems than inner planets.
The reason for different composition of planets has to do with how the solar system formed. In the early solar system, there was a disk of material rotating around the Sun, from which the planets eventually formed. However, to form planets required some kind of initial clump in the protoplanetary disk. These clumps were probably formed from collisions of solid particles. Different elements become solid at different temperatures: the most common elements, hydrogen and helium, never became solid, but hydrogen compounds (like water) can solidify at colder temperatures, like those in the outer solar system. In the inner solar system, it was too hot for these compounds to solidify; only rocks and metals can solidify at these temperatures. Hence, only small planetesimals formed in the inner solar system.
In a game of shuffleboard (played on a horizontal surface), a puck is given an initial speed of 6. 0 m/s. It slides a distance of 9. 0 m before coming to rest. What is the coefficient of kinetic friction between the puck and the surface?.
The coefficient of kinetic friction between the puck and surface id 0.20.
What is coefficient of kinetic friction?
Coefficient of kinetic friction is the ratio between frictional force present in the motion of two surfaces that are in contact to the normal force that presses the two surface together.
It is calculated mathematically as: μ = F/N, where
F= frictional force and N= normal force.
v2 = u2 +2as
0= 62 + 2a9
18a + 36= 0
18a = -36
a= -2
friction = μ × normal force
or friction =ma
ma= μN
ma= μ(mg)
μ = a/g where g = 9.8 N
μ= -2/9.8
⇒0.20.
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Many animals use __?__to find prey.
2. A porpoise sends out an ultrasonic burst and hears the echo off his favorite food in 0.13 seconds. How far away is the food source? Assume that sound travels at 1,530 m/sec in water.
Answer:
Below
Explanation:
"echo location"
The sound travels the distance, d , to the food and back for a total distance of 2d
2d = 1530 m/s * .13 s
d = ~ 99 m away
Explain why increasing temperature from 3°C to 6°C does not double temperature. In Charles law.
Celsius does not measure at an absolute temperature , hence increasing temperature from 3°C to 6°C does not double temperature. In Charles law.
Heat or bloodless is measured in terms of temperature. It demonstrates how warmth electricity certainly flows from a warmer body to a cooler body and may be expressed in phrases of any range of arbitrary scales (one at a decrease temperature).
A match is burning at a far greater temperature than an iceberg, yet an iceberg has a considerably better total warmth electricity than a in shape. Temperature isn't always similar to the electricity of a thermodynamic system.
Temperature, along side strain, density, and different like qualities, is known as an excessive belongings as opposed to vast functions, together with mass or extent—one this is independent of the quantity of stuff being addressed.
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scientists attribute some global warming and cooling periods to the culmination of the effects of the milankovitch cycles. milankovitch cycles are variances in earth's axis and orbit that correspond to the earth's position in relation to the sun. classify each constituent of the milankovitch cycles as pertaining to orbital eccentricity, axial tilt, or axial precession.
Each constituent of the Milankovitch cycles as pertaining to orbital eccentricity, axial tilt, or axial precession are classified accordingly.
The constituents of the Milankovitch cycles as pertaining to orbital eccentricity are:
Path varies from round to elliptical.100000 year cycleThe earth's changing distance from sun during orbit impacts the climate , sometimes producing glacial periods.The constituents of the Milankovitch cycles as pertaining to axial tilt are:
41000 year cycle.Changes to earth's orientation to the sun affect the severity of seasons.The angle of earth's tilt change as it spins on its axis.When the angle from vertical is greater , seasons become greater in variability.The constituents of the Milankovitch cycles as pertaining to axial precession are:
20000 year cycle.The earth "wobbles" on its axis, which can change the orientation of the axis with celestial bodies.Therefore, each constituent of the Milankovitch cycles as pertaining to orbital eccentricity, axial tilt, or axial precession are classified accordingly.
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The scientific method is a process, consisting of steps that need to be followed in order to answer questions to observations we may have about the world around us.
true or false
True.
According to Merriam-Webster:
"principles and procedures for the systematic pursuit of knowledge involving the recognition and formulation of a problem, the collection of data through observation and experiment, and the formulation and testing of hypotheses"
Answer:
True
Explanation:
The SCIENTIFIC METHOD is the process of establishing facts through experiments and tests. The process includes getting an observation, making hypothesis, making a prediction, implementing the experiment and submitting the analysis report.
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An air-filled toroidal solenoid has a mean radius of 15.0cm and a cross-sectional area of 5.00cm2 . When the current is 12.5A , the energy stored is
0.390J .How many turns does the winding have?
The number of turns the winding have in an air-filled toroidal solenoid that has a mean radius of 15.0cm and a cross-sectional area of 5.00cm2 is 2745 turns
According to Ampere's law,
B = μo N I / 2 π r
Φ[tex]_{B}[/tex] = B A
Φ[tex]_{B}[/tex] = μo N I A / 2 π r
B = Magnetic field
μo = Absolute permeability of free space
N = Number of turns
I = Current
r = Radial distance
A = Cross sectional area
U = Energy stored
U = 1 / 2 L I²
L = 2 U / I²
L = N Φ[tex]_{B}[/tex] / I
μo = 4 π * [tex]10^{-7}[/tex] H / m
U = 0.39 J
r = 15 cm = 0.15 m
I = 12.5 A
A = 5 cm² = 5 * [tex]10^{-4}[/tex] m²
Equating,
2 U / I² = N Φ[tex]_{B}[/tex] / I
2 U / I² = μo N² I A / 2 π r I
4 π r U / μo I² A = N²
N² = ( 4 * 3.14 * 0.15 * 0.39 ) / ( 4 * 3.14 * [tex]10^{-7}[/tex] * 12.5² * 5 * [tex]10^{-4}[/tex] )
N² = 0.74 / 9812.5 * [tex]10^{-11}[/tex]
N² = 7.54 * [tex]10^{6}[/tex]
N = 2.745 * 10³
N = 2745 turns
Therefore, the number of turns the winding have are 2745 turns
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The parallax angle for the star Hadar is 0.010 arcseconds. How far away is Hadar?
The parallax angle for the star Hadar is 0.010 arcseconds. 100 PC far away is Hadar.
Parallax angle is a displacement or distinction in the apparent function of an item considered alongside two one-of-a-kind lines of sight and is measured by the attitude or semi-perspective of inclination among those two lines. because of foreshortening, close-by objects display a bigger parallax than farther items when found from distinct positions, so parallax may be used to determine distances.
To a degree of big distances, including the gap between a planet or a star from Earth, astronomers use the precept of parallax. right here, the term parallax is the semi-perspective of inclination between sightlines to the megastar, as observed while Earth is on contrary sides of the solar in its orbit. those distances shape the lowest rung of what's called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial items, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder.
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A charming friend of yours who has been reading a little bit about astronomy accompanies you to the campus observatory and asks to see the kind of star that our sun will ultimately become, long, long after it has turned into a white dwarf. Why is the astronomer on duty going to have a bit of a problem satisfying her request?.
Following cooling, a white dwarf becomes too cold and dark to emit visible light.
What is white dwarf?
Like our Sun, medium-mass stars generate helium by fusing hydrogen within their cores. Our Sun is now performing this. An outward pressure results from the heat the Sun produces during the nuclear fusion of hydrogen into helium. The Sun will run out of hydrogen in its core in about 5 billion years.
The Sun begins to collapse when it runs out of hydrogen to fuse, tipping the scales in favor of gravity. However, compacting a star makes it heat up once more, allowing it to fuse what little hydrogen is left in a shell surrounding its core.
We can learn about the age of the universe from white dwarfs. Our galaxy and the age of the universe would be lowered if we could calculate how long it takes for a white dwarf to cool into a black dwarf.
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Please help really confused?
At point A the spinning wheel will experience least centripetal force.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Centripetal force is applied on object depends on the centre and object distance. So B will experience maximum force while A is least.
At point A the spinning wheel will experience least centripetal force.
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the drawing shows a skateboarder moving at 6.90 m/s along a horizontal section of a track that is slanted upward by 0
The maximum height H to which she rises above the end of the track that is slanted upward by 48° above the horizontal at its end is 1.11 m
KE = 1 / 2 m v²
PE = m g h
According to law of conservation of energy,
KE ( Initial ) + PE ( Initial ) = KE ( Final ) + PE ( Final )
h ( Initial ) = 0
v ( Initial ) = 6.9 m / s
g = 9.8 m / s²
h = 0.4 m
1 / 2 m vi² + m g hi = 1 / 2 m v² + m g h
1 / 2 m vi² = 1 / 2 m v² + m g h
vi² = v² + 2 g h
6.9² = v² + ( 2 * 9.8 * 0.4 )
v² = 47.61 - 7.84
v² = 39.77 m / s
H = vi² sin²θ / 2 g
θ = 48°
H = 39.77 * sin²48° / ( 2 * 9.8 )
H = 21.78 / 19.6
H = 1.11 m
Therefore, the maximum height H to which she rises above the end of the track is 1.11 m
The given question is incomplete. The complete question is;
The drawing shows a skateboarder moving at 6.9 m/s along a horizontal section of a track that is slanted upward by 48° above the horizontal at its end, which is 0.40 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
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How long does it take to use 266 W of power pushing at 113 N for a distance of 9 meters?
The power pushing at 113 N for a distance of 9 meters. The time taken is 0.22 seconds.
Power :
Power is defined as the speed at which work is performed on an object.
work done = Force x Distance
Power = Work done/ Time
Power = (Force x Distance)/Time
Power = 226 Watt
Force = 113 N
Distance taken = 9 meters
To calculate power we use :
Power = (Force x Distance)/Time
266W = (113N x 9s)/Time
Time = 266W/(113N x 9m)
Time = 266W/(113N x 9m)
Time = 0.22 seconds
The power pushing at 113 N for a distance of 9 meters. The time taken is 0.22 seconds.
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write the formula for newton's method and use the given initial approximation to compute the approximations x1 and x2
Using Newton's method , the approximations value of x₁ and X₂ are 7.1 and 7.0 respectively.
Newton's method: Newton’s method is a procedure for approximating the solutions of an equation f(x) =0. These are also called the zeros of f. Newton’s method is an iterative procedure that finds an approximation to a rootof f(x) =0 and then uses the approximation to help find a better approximation. This gives a list of numbers x1, x2, x3, . . . which we call successive approximations. We begin by explaining the main step of method with shows us how to find xn+1 from xn.
Given an approximation xn, compute the next approximation by xₙ+1 = xₙ− f(xₙ)/f'(xₙ).•
We have given that,
f(x) = x²−2x−35, and x₀= 6
approximation relation for succive approximation
is xₙ + 1 = xₙ − (xₙ2 - 2xₙ- 35) / 2xₙ− 2
Now , we compute the values of x1 and X2 using approximation relation
put n= 0 , in above formula we get
X₁ = x₀- ( x₀²- 2x₀ - 35)/2x₀ -2
using initial condition, x₁ = 6 - ( 36-12-35)/10 = 7.1
again put, n= 1
x₂ = x₁ - ( x₁ ² - 2x₁ -35)/2x₁ -2 = 7.1 - ((7.1)² - 14.2 -35)/12.2 = 7.00
Hence, the value of first succive approximation (x₁) is 7.1 and second approximation (x₂) is 7.00
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Complete Question:
Write the formula for Newton's method and use the given initial approximation to compute the approximations x1 and x2.
f(x)=x2−2x−35, x0 =6
Write the formula for Newton's method for the given function. Choose the correct answer below.
xn+1=xn−(xn2−2xn−35 )/ 2xn−2
Use the given initial approximation to compute the approximations x1 and x2.