The correct answer is option C:
According to modern ideas and observations, the location of the center of our expanding universe explains that the universe does not have a center.
Our universe is composed of three kinds of substances that are dark matter, normal matter, and dark energy.
Everything in the universe is made of normal matter i.e. planets, stars, human beings, and all other visible objects.
Astronomers have theorized that the universe is expanding at a faster rate. Between any two given points, the distance of the universe is increasing and so we can predict that the universe will be 2x in size after ten billion years.
In general, the universe has no central point and it is expanding continuously because of a dark, mysterious force that is pulling the universe apart.
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remember that when dealing with collisions in 2-dimensions, momentum is conserved in each dimension. two pucks are sliding on a frictionless tabletop. block a (mass 3.94 kg) is moving to the east ( x direction) at 2.50 m/s. block b (mass 4.73 kg) is moving to the north ( y direction) at 3.00 m/s. assume the system to be both block a and block b. (note: it could be useful to make a drawing of the situation.) what is the x-component of the total momentum of the system before the collision?
The x-component of the total momentum of the system before the collision is 9.850 kgm/s.
P = MV
3.94 x 2.50 m/s = 9.850kgm/s.
The definition of momentum is "mass in motion." Since every item has mass, if it is moving, it must have momentum because its mass is in motion. The amount of motion and the speed of the motion are the two factors that determine how much momentum an item possesses. An object's linear momentum sometimes referred to as translational momentum or simply momentum is the product of its mass and velocity.
It has both a magnitude and a direction, making it a vector quantity. If an item has mass m and velocity v, then it has momentum p. Momentum can be defined as the amount of motion. Quantity may be quantified in this case since an object has momentum if it is traveling and mass.
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rocky the flying squirrel is carrying a nut of mass 0.5 kg while flying horizontally at a height of 15 m above the ground at a speed of 12 m/s. bullwinkle is eagerly awaiting the delivery of the nut on the ground. rocky releases the nut as he is directly above bullwinkle. how far from bullwinkle will the nut land if bullwinkle does not move
The nut distance from the Bullwinkle after uniform motion is 21 m.
We need to know about the uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule
vt = vo + a . t
vt² = vo² + 2a . s
s = vo . t + 1/2 . a . t²
where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.
From the question above, the parameters given are
m = 0.5 kg
s = 15 m
vx = 12 m/s
vo = 0 m/s
a = g = 9.8 m/s²
Find the time taken of the nut for landing
s = vo . t + 1/2 . a . t²
15 = 0 + 1/2 . 9.8 . t²
t² = 3.06
t = 1.75 s
Find the distance of nut in horizontal direction
vx = x / t
12 = x / 1.75
x = 12 . 1.75
x = 21 m
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what is the conversion efficiency (power coefficient) from power in the wind to electrical power output for a modern highly engineered horizontal axis high-tip-speed two blade wind turbine? group of answer choices
The conversion efficiency from the power in the wind to electrical power output for a modern highly engineered two blade wind turbine is 35 % to 45%.
What is power coefficient and how the conversion efficiency from power in wind to turbine is so?Power coefficient is similarity in relation to power just combining the flow coefficient and head coefficient.Power coefficient is denoted by Cp and whose equation is like Cp= f( Vwind) where V is the velocity of the wind.Here in the question is asked the conversion efficiency from power in wind to the power in wind turbine.So the conversion efficiency from the power in the wind to the electrical power output for a modern highly engineered two blade wind turbine is 35% to 45%.To know more about power coefficient visit:
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a car's bumper is designed to withstand a 5.40 km/h (1.5-m/s) collision with an immovable object without damage to the body of the car. the bumper cushions the shock by absorbing the force over a distance. calculate the magnitude of the average force on a bumper that collapses 0.225 m while bringing a 890 kg car to rest from an initial speed of 1.5 m/s.
The average force is F = 2722.5N
This law of interaction states that when one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body. This is the law of action and reaction, which helps explain why you feel the impact when you collide with another bumper car.
When the car hits something at low speed, the foam and fenders absorb the energy, pushing the bumper back and using the crumple zone to cushion the impact. Shattering the bumpers, fenders, and foam limits the damage you can do to the cars and the people inside them. means equal to the sum.
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Look at the diagram. Calculate the Rf value for sample 7. Give your answer to two decimal places.
The Rf value of sample 7 is 0.94.
What are Rf values?Rf (retention factor) values are values that are used to identify compounds in thin-layer chromatography.
Rf values are obtained by taking the ratio of the distance traveled by the solvent (solvent front) and that traveled by the substance or unknown compound.
Rf = distance traveled by compound / distance traveled by the solventThe Rf value of sample 7 is calculated below:
distance traveled by compound = 33 mm
distance traveled by the solvent = 35 mm
Rf value = 33 mm/ 35 mm
Rf value = 0.94
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Two people are playing soccer. The kinetic energy of each soccer player depends on the soccer players mass and speed. Compare the two soccer players
The two soccer players kinetic energy are 1 / 2 m1 v1² and 1/ 2 m2 v2² for soccer player 1 and 2 respectively
KE = 1 / 2 m v²
KE = Kinetic energy
m = Mass
v = Velocity
Let the mass and velocity be m1 and v1 respectively for soccer player 1. Let the mass and velocity be m2 and v2 respectively for soccer player 2.
For soccer player 1,
m = m1
v = v1
KE1 = 1 / 2 m1 v1²
For soccer player 2,
m = m2
v = v2
KE2 = 1 / 2 m2 v2²
KE ∝ m
KE ∝ v²
The kinetic energy is directly proportional to mass and velocity squared. So increase in any of these factors will increase the kinetic energy and similarly decrease in any of these factors will result in decrease of kinetic energy.
Therefore, the two soccer players kinetic energy are 1 / 2 m1 v1² and 1 / 2 m2 v2² for soccer player 1 and 2 respectively
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Answer:
Cristiano Ronaldo SUII
Explanation:
is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) is it possible for the electric force on a charge moving in an electric field to be zero? (c) is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?
a) Yes, provided that the speed is parallel to the magnetic field.
b) No, it is not possible electric field to be zero.
c) No. the magnetic force can be zero.
How do magnetic forces work?Magnets, which can be used to repel or attract other things, exert a force known as magnetism. One of the fundamental forces of nature, electromagnetic, is one of the components of this potent physical phenomenon. A magnetic field is produced when electrically charged particles, which are present in all matter, move.
Briefing:a)Yes, provided that the speed is parallel to the magnetic field.
b) No, the electric force acting on a charge travelling in an electric field cannot be zero since the electric field's amplitude and direction are independent of the motion or velocity of the charged particles.
c) No, the electric force cannot be zero because it is unaffected by the motion of the particles, but the magnetic force can be zero.
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the floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.36 with the floor. if the train is initially moving at a speed of 45 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?
24.8 m is the shortest braking distance.
On the horizontal axis, we dread the force of friction (fr) that prevents the train from moving and accelerating.
Y axis
N- W = 0
N = W = mg
explanation?
In order to fix this issue, we must apply Newton's second law to the boxes, with the norm vertically up and the weight vertically down.
Write the equation for each axis. On the horizontal axis, we dread the force of friction (fr) that prevents the train from moving and accelerating.
Y axis
N- W = 0
N = W = mg
X axis
-Fr = m a
-μ N = m a
-μ mg = ma
a = μ g
a = - 0.36
a = - 3.14 m/s²
Utilizing the kinematics equations, we determine the distance.
(Vf2 - Vo2) / 2 a = Vf2 = Vo2 + 2 an
The speed of the train is zero (Vf = 0) when it stops.
Vo=45 km/h (1000 m/km) (1 h 3600 s)= 12.5m/s
x = ( 0 - 12.5²) / 2 (-3.14)
x= 24.88.8 m
The shortest braking distance is 24.8 m
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a cubical box of mass 2kg with each side 2 cm is lying on the ground. Calculate the pressure exerted by the block on the ground
Answer:
25000Nm⁻² using rounded g figure
Explanation:
The box is in cm. It needs to be converted into SI metres.
1m = 100cm
1cm = ( 1 / 100 )m
2cm = ( 1 / 50 )m
A = ( 1 / 2500 )m²
Assume that g = 10ms⁻¹. Use your own definition.
F = 10N
P = F / A
P = 10N( 2500 )m⁻²
25000Nm⁻²
Answer:
Explanation:
Given:
m = 2 kg
a = 2 cm = 0.02 m
g =9.8 m/s²
_______________
P - ?
Area of the cube:
S = a² = 0.02² = 0,0004 m²
Gravity:
F = m·g = 2·9.8 = 19.6 N
Pressure:
p = F / S = 19.6 / 0,0004 = 49 000 N/m²
when the pendulum bob is at its maximum height (farthest from the center of the earth), is the gravitational potential energy of the bob-earth system at a maximum, minimum or some value in between? briefly explain.
Both gravitational potential energy (PE) and kinetic energy (KE) are present on a swinging pendulum bob. The KE is at its highest and the PE is zero when the bob is in its lowest position. The KE is zero and the PE is at its highest value when the bob is in its highest position on both sides.
When does the pendulum's speed reach its highest point?The pendulum moves at its fastest while it is passing through the middle position. We could interpret this in terms of energy conservation. Bob is at his shortest height when he is in the average position. When Bob is positioned at an extreme, such as the right, it is slightly higher than when it is in the middle.
What happens to a pendulum's length when it is full?The bob's center of mass serves as the standard for determining the pendulum's "length." The center of gravity of the bob would fluctuate in a convoluted manner as the mercury drained out of a simple spherical bob with a small hole in the bottom. The center of gravity would be in the middle of the bob when it is totally full.
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an interference pattern is produced by four parallel and equally spaced narrow slits. by drawing appropriate phasor diagrams, explain why there is an interference minimum when the phase difference from adjacent slits is:
The minimum interference when the phase difference from adjacent slits is ( A1 -A2)².
The amplitude of a periodic variable is the degree of its change in a single duration. The amplitude of a non-periodic signal is its important as compared with a reference cost. there are various definitions of amplitude, which are all features of the magnitude of the variations between the variable's excessive values.
Let A1 be the amplitude of the 1st wave and A2 be the amplitude of the 2nd wave.
Let the resultant amplitude be A.
the formula of interference, we get,
A= (A1)²+(A2)²+ 2×A₁× A₂ (cos theta)
When theta = 180 degrees = π radian, cos π= -1
Putting the value of cos theta in the equation we get,
A= (A1)² +(A2)² - 2×A1×A2
A= ( A1 -A2)²
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If an object is thrown horizontally, travels with an average x-component of its velocity equal to 5m/s, and does not hit the ground, what will be the x-component of the displacement after 20s?
Answer:
100 m
Explanation:
5 m/s * 20 s = 100 m
an ice hockey forward with mass 70.0 kg is skating due north with a speed of 5.5 m/s. as the forward approaches the net for a slap shot, a defensive player (mass 110 kg) skates toward him in order to apply a body-check. the defensive player is traveling south at 4.0 m/s just before they collide. if the two players become intertwined and move together after they collide, in what direction and at what speed do they move after the collision? friction between the two players and the ice can be neglected.
The speed of the two players after the collision is 0.31 m/s in a direction of due south.
What is the final speed of the two players?The final speed of the two players after the collision is calculated as follows.
Apply the principle of conservation of linear momentum;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
m₁ is the mass of the first playerm₂ is the mass of the second playeru₁ is the initial velocity of the first playeru₂ is the initial velocity of the second playerv is the common speed of both players after the collision.(70 x 5.5) + (-110 x 4) = v(70 + 110)
385 - 440 = 180v
-55 = 180v
v = -55/180
v = -0.31 m/s
Thus, the direction of the speed of the two players after the collision is due south.
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line spectra from all regions of the electromagnetic spectrum, including the paschen series of infrared lines for hydrogen, are used by astronomers to identify elements present in the atmospheres of stars. calculate the wavelength of the photon emitted whe
The wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3 is 1282 nm.
From the Rydberg's formula;
1/λ = R (1/[tex]n^{2} _{final}[/tex] - 1/[tex]n^{2} _{initial}[/tex])
R = 1.097 ×[tex]10^{7} m^{-1}[/tex]
nfinal = 3
ninitial = 5
Calculating the wavelength of the photon by substituting values, in equation 1/λ = R (1/[tex]n^{2} _{final}[/tex] - 1/[tex]n^{2} _{initial}[/tex]) , we get:
1/λ = 1.096776×[tex]10^{7} m^{-1}[/tex] (1/[tex]3^{2}[/tex] - 1/[tex]5^{2}[/tex])
1/λ = 1.096776×[tex]10^{7} m^{-1}[/tex] (1/9 - 1/25)
λ = 1.282 × [tex]10^{-6}[/tex] m
λ = 1282 nm
Therefore, the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3 is 1282 nm.
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To find the density of an object you would use a graduated cylinder to find what characteristic of the obiect? A)mass b)length c)volume d)weight
Answer:
C Volume
Explanation:
You would use a graduated cylinder with liquid in it to see how much is displaced when the object is placed in it to determine the volume of the object
Pls help me
I’m stuck I tried searching the internet but it didn’t work
According to the given statement A toy car that initially increases its speed, travels constant speed, and then decreases its speed.
The correct option is B.
Describe speed using an example:Speed, expressed in terms of meters per second, is the rate at which an object's location changes. An item moves one meter in one second, for instance, if it starts at the origin and moves three meters in three seconds. Simple division of time by distance yields the equation for speed.
What is a speed measurement tool?Speedometers are tools that show a car's speed and are frequently paired with odometers, which keep track of the distance driven.
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The complete question is-
A student performs an experiment in which the horizontal position of a toy car is recorded on ticker tape from a device that places dots on the tape in equal time intervals. The series of dots in the figure represents the motion of an object moving from the negative direction to the positive direction along the horizontal direction. The time interval between each recorded dot is 1s. Which of the following experiments could the student have conducted to create the data shown on the ticker tape?
A toy car that initially increases its speed, travels at a constant speed, and then increases its speed again.
B-A toy car that initially increases its speed, travels at a constant speed, and then decreases its speed.
C-A toy car that initially decreases its speed, and then increases its speed.
D-A toy car that initially decreases its speed, travels at a constant speed, and then increases its speed.
True or false. Objects tend to stay moving because of a force called inertia
Answer:
true
Explanation:
Kinetic theory told us that gas particles are moving constantly and bumping into anything in their path. The collisions of these particles in the gas result in ___________ .
a
Energy conversion
b
Pressure
c
Creation of new forms of matter
d
Potential energy
According to the research, the correct option is d. Kinetic theory told us that gas particles are constantly moving and bumping into anything in their path. The collisions of these particles in the gas result in Potential energy.
What is Kinetic theory?It is the model of matter that, starting from the definition of an ideal gas from the point of view, explains the behavior of matter at the molecular level when it is subject to certain conditions.
In this sense, it studies the behavior of molecules and their interactions, where the energy that is capable of being developed during the collision of small particles is first converted into potential energy associated with the position of a body.
Therefore, we can conclude that the kinetic theory explains the interactions that occur in gas particles, where kinetic and potential energy can influence their state.
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when the radius of a circular phase space plot changes, what does this mean? a. momentum is conserved. b. momentum is not conserved. c. energy is not conserved. d. energy is conserved.
Answer is b, momentum is not conserved.
Explanation:
L = r × p
So when the radius of a circular phase space plot changes, the Momentum is not conserved because farther the mass is from the center of rotation, the larger the angular momentum.
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an ideal parallel-plate capacitor consists of a set of two parallel plates of area a separated by a very small distance d. when the capacitor plates carry charges q and -q, the capacitor stores energy u0. if the separation between the plates is doubled, how much electrical energy is stored in the capacitor?
Electrical energy is energy that has to do with forces acting on electrically charged particles and their motion.
What is mean by electrical energy?The ability of an atom's charged particles to initiate an activity or move an object is known as electrical energy. Electrical energy is produced by the transfer of electrons between atoms. Electrical energy powers your toaster and phone charger every time you plug them into a wall outlet.
Electrical energy is energy that has to do with forces acting on electrically charged particles and their motion.
The capacitance of a capacitor is given by the following formula
C=∑0A/d
And the electric potential energy stored in a capacitor is given by
∪[tex]Q2[/tex]/2AC
Applying these formula to the given variables, the initial potential energy becomes
∪[tex]0[/tex]=[tex]Q2/2=d/[/tex]∑A
If d becomes 2d, then potential energy becomes
∪0=[tex]Q2/2[/tex] 2D/∑A=2∪0
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HELP!
Noble gases are the ____________________.
A. most reactive of all elements
B. least consistent of all elements
C. most consistent of all elements
D. least reactive of all elements
Answer: Most consistent of all elements (if consistency here denotes stability)
if not, then the answer will be (D)
Explanation:
Nobel gasses have full outermost electron shells which means that they are very stable and do not need to lose, gain, or share electrons to gain stability. So they do not react with other elements to form ionic or covalent bonds
use as much force as possible to accomplish the task at hand. do not apply pressure between instrumentation strokes. group of answer choices both statements are true. both statements are false. the first statement is true; the second statement is false. the first statement is false; the second statement is true.
Three different activation stroke types are employed during periodontal instrumentation: the assessment stroke (exploratory stroke), the calculus removal stroke (scaling stroke), and the root planing stroke.
What strokes are used during instrumentation?
It is advised to maintain cerebral perfusion pressure between 61 and 80 mmHg if the systolic blood pressure is greater than 180 mmHg and there is proof or reason to suspect that intracranial pressure is raised. Because a standard curet blade positioned for a vertical or oblique stroke is frequently too large to adapt to root curvatures or for deep insertion in the pocket, especially in narrow pockets or regions with tight tissue tone, horizontal strokes are essential for successfully removing calculus in deep pockets. On the mesial, facial, distal, and lingual surfaces of the front teeth as well as the mesial and distal surfaces of the posterior teeth, vertical strokes are utilized.To clear the periodontal pocket and remove dental calculus, there are three main categories of electronic devices. Head is essentially upright.Head in the least strenuous vertical and horizontal posture.In order to avoid neck and head pain, the eyes are pointed downward. The thumb is positioned on the opposite side of the instrument from the four fingers.Dental instruments are handled using the standard pen grip, which involves holding a pen between the tips of the thumb and forefinger and the lateral side of the distal (final) phalanx of the middle finger. No matter where we position our fulcrum, we should always apply lateral pressure, or pressure to the side of the instrument.With this technique, you may make sufficient strokes without slipping off the tooth and damaging delicate tissue. The blade's shape is the primary distinction between a scaler and a curette in terms of design.A curette's blade is semicircular in cross section, whereas a scaler's blade is triangular.To learn more about instrumentation stroke refer
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How do these forces affect the car's
movement?
Thrust, Lift, Drag, and Weight are four opposing forces that affect every vehicle, whether it's a car, truck, boat, airplane, helicopter, or rocket.
What is force?A force is an influence that can cause an object's motion to change. A force can cause a mass object to change its velocity, or accelerate. Intuitively, force can be described as a push or a pull. A force exist as a vector quantity because it has both magnitude and direction. A mass object's velocity changes when it is pushed or pulled. Force is an external agent that can change the state of rest or motion of a body. It has a magnitude as well as a direction. The term "force" has a specific meaning. At this level, it is perfectly acceptable to refer to a force as a push or a pull.To learn more about force, refer to:
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If a magnifying glass uses a convex lens of focus length 6.25 cm when it is held 5.20 cm in front of an object what is the image distanceMind your minus signs Unit cm
Answer:
30.95 cm
Explanation:
The focal length f, the object distance do, and the image distance di are related with the following equation:
[tex]\frac{1}{f}=\frac{1}{d_0}+\frac{1}{d_i}[/tex]So, replacing the values, we get:
[tex]\frac{1}{6.25}=\frac{1}{5.20}+\frac{1}{d_i}[/tex]Then, solving for di, we get:
[tex]\begin{gathered} \frac{1}{6.25}-\frac{1}{5.2}=\frac{1}{d_i} \\ -\frac{21}{650}=\frac{1}{d_i}_{} \\ -\frac{650}{21}=d_i \\ -30.95\operatorname{cm}=d_i \end{gathered}[/tex]Therefore, the image distance is 30.95 cm
In general, how should you shuffle the mass in a rotating object to decrease its overall moment of inertia?.
Bring mass up against the axis of rotation. Consequently, a rotating object's overall moment of inertia will decrease due to its mass. The axis and the mass narrows as the mass moves closer together.
A measure of a body's propensity to resist angular acceleration that is calculated by summing the products of each particle's mass and square of its distance from the axis of rotation moment of inertia
A line along which an item rotates is referred to as its axis of rotation (also known as its axis of revolution). That line is typically fictitious in physics and calculus. The distance from the object's outside border to the axis of rotation is known as the radius of rotation.
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Ethan slid a glass of OJ for peter across a counter with a speed of 2.1 m/s unfortunately peter missed it if the countertop was 1.1m above the floor how long did it take for the glass to hit the ground
Answer:
It takes 0.47 seconds for the OJ to reach the ground.
Explanation:
d = vi*t + (1/2)at^2
(-1.1) = (0)t + (1/2)(-9.8)t^2
-1.1 = -4.9t^2
0.22445 = t^2
0.47s = t
Mutations can occur randomly during DNA replication. Suppose DNA replication is occurring in a cell. If DNA replication occurs
correctly, the following strand will be produced.
If a point mutation occurs during DNA replication, which of these could represent the mutated strand produced instead?
OA.
ATG GAC CAT TGG C
ATG GAC CAA CTT TCG GC
ATG CGT CAT TTC GGC
ATG GAC CTT TTC GGC
B.
(C.
ATG GAC CAT TTC GGC
OD.
. gun sights are adjusted to aim high to compensate for the effect of gravity, effectively making the gun accurate only for a specific range. (a) if a gun is sighted to hit targets that are at the same height as the gun and 100.0 m away, how low will the bullet hit if aimed directly at a target 150.0 m away?
The problem describes a situation where a bullet is launched at a certain angle respect to the horizontal to hit in the target, given the launching conditions and the distance to the target. The formulas to compute the magnitudes involved in the projectile motion are
x=[tex]v0[/tex] cos0 t
Y=[tex]V0[/tex] sin0 t
xm=[tex]v0[/tex]² sin 20/g
[tex]Xm[/tex] is the maximum horizontal distance the object can reach when it returns to the ground (or launching height).
let's check if X is computed correctly .
The set of data is correct. We can now proceed to the required distance. We know the bullet is shot directly to the target, so the angle is 0, keeping the same speed. The new maximum distance is 150 m, so we can compute the time needed to complete the flight
since
Let's find the time from the formula
X=[tex]V0[/tex] cos0 t
t=[tex]Xm[/tex]/[tex]V0[/tex] cos0
t=150/100=1.5
Y=(9.8)(0.66)²÷2
Y=-2.134
The bullet will hit 2.134 meters below the target
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1. PE = ?
m = 0.6 kg
g= 9.8 m/s²
h = 35 m
WORKS
Answer:
Explanation:
Potential Energy = m * g * h = .6 * 9.8 * 35 = 205.8 J
Two uniform cylinders are machined out of solid aluminum. One has twice the radius of the other. If both are placed at the top of the same ramp and released, which is moving faster at the bottom?.
Both cylinders will reach the same speed since speed is independent of mass and radius.
Radius of smaller cylinder = R1
Radius of bigger cylinder = R2
their masses = m1/m2 = [tex]\frac{R1}{2R1} ^{2}[/tex]
From law of conservation of energy we have
[tex]mv^{2} /2 + Iw^{2}[/tex] = mgh
[tex]1/2 mv^{2}[/tex] + [tex]m\frac{R}{L}[/tex] × [tex]\frac{x}{y}[/tex] = mgh
3/4 v2 = gh
v= [tex]\sqrt{4/3gh}[/tex]
Since from the above relation, speed is independent of mass and radius, so both cylinders have same speed.
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Neither of the two cylinders moves faster at the bottom. Both cylinders move with the same velocity at the bottom.
By the formula for conservation of energy, for a solid cylinder placed at the top of a ramp and rolling down to the bottom, we have
The kinetic energy of linear motion + rotational kinetic energy = potential energy (1)
Kinetic energy due to linear motion (of the center of mass of cylinder)= [tex]\frac{1}{2} mv^{2}[/tex]
Rotational kinetic energy = [tex]\frac{1}{2}Iw^{2}[/tex]
m = mass of cylinder, v = velocity of the center of mass of the cylinder
I = moment of inertia of solid cylinder = [tex]\frac{1}{2}mR^{2}[/tex] (R = radius of cylinder)
angular velocity w = v/R
g = acceleration due to gravity, h= height of the ramp
From equation (1)
[tex]\frac{1}{2}mv^{2}+ \frac{1}{2}Iw^{2} = mgh[/tex]
⇒[tex]\frac{1}{2}mv^{2}+\frac{1}{2}(\frac{1}{2}mR^{2}* \frac{v^{2} }{R^{2} } ) = mgh[/tex]
⇒[tex]\frac{1}{2}mv^{2}+\frac{1}{4}mv^{2}=mgh[/tex]
⇒[tex]\frac{3}{4}[/tex][tex]mv^{2} =mgh[/tex]
⇒v=√(4gh/3) (cancel m on both sides)
Thus we see the velocity at the bottom of the sloping ramp that is v is independent of the mass or radius of the solid cylinders and only depends on the height of the ramp and acceleration due to gravity.
Thus both cylinders reach the bottom with the same velocity.
What is the moment of inertia of a body:
brainly.com/question/15246709
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