The mass of the bob has no bearing on the pendulum's time period.The time duration would therefore remain the same if the mass of the bob doubled.
Solve the problem ?
The equation of motion for the pendulum can be found by using Newton's second rule for rotational systems: =ImgsinL=mL2d2dt2 and then rearranged as d2dt2+gLsin=0 d 2 d t 2 + g L sinIf the angular displacement's amplitude is sufficiently modest, the tiny angle... The length of the rope and the acceleration caused by gravity determine the time it takes for a simple pendulum to swing.When a simple pendulum's length is increased by four times, its period doublesWe currently have the simple pendulum era, which is the simple one to square root of and upon you.Now that the length has been extended, terrible food, we will have an easy quality to buy into L. A. Banjo's square root.This will be equivalent to dividing my by L squared and G by 4²That also is.Since the only factor in this situation is time, we will go into great detail.So, if the basic pendulum's length is raised by a factor of four, its time period will also double.That choice will be the right response. On Earth, a pendulum's swing is only greatly influenced by the length of its string.Students could question why a pendulum's period is solely determined by the length of the string.
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a 4.0 kg block on a horizontal, frictionless surface is connected by a massless string and a massless, frictionless pulley to a hanging mass. for what value of the hanging mass does the block accelerate at 1.8 m/s2 ?
13a value of the hanging mass does the block accelerate at 1.8 m/s2
For 8 kg mass,
m 1 g - T = m 1 a
8g - T = 8a —————(I)
For 5 kg mass,
T - m 2 g = m 2 a
T - 5g = 5a —————(II)
Adding both equations, we get
8g - 5g = 13a
On a surface with no friction, is there acceleration?The constant velocity of the body on the frictionless surface is represented by the frictionless surface acceleration. No net force on the moving object can stop it from going when the surface is frictionless. As a result, the body keeps moving at the same speed. The skater has no net acceleration if no forces are operating on him and he is on a frictionless surface. The acceleration must be zero since the skier must have mass. If there is no acceleration when an item is moving, its velocity stays constant.
We must understand that acceleration always occurs in areas where there is friction. There are several types of forces at work on moving objects.
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What element has 4 electrons 3 protons and 6 neutrons
The element that has 4 electrons, 3 protons and 6 neutrons is lithium ion.
What is an element?An element is one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means and made up of atoms all having the same number of protons.
The atom of an element is made up of three subatomic particles namely;
ProtonElectronNeutronIn a neutral element, the number of protons and electrons are the same i.e. equal. According to this question, an element has 4 electrons, 3 protons and 6 neutrons.
The element in the periodic table with 3 protons is Lithium. This means that the element is lithium ion because it has gained one electron.
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A father fashions a swing for his children out of a long rope that he fastens to the limb of a tall tree. As one of the children swings from this rope that is 5.70 m long, his tangential speed at the bottom of the swing is 9.10 m/s.What is the centripetal acceleration, in m/s2, of the child at the bottom of the swing?
Given,
The length is r=5.70 m
The tangential speed is r=9.10 m/s
The centripetal acceleration is:
[tex]\begin{gathered} a=\frac{v^2}{r} \\ \Rightarrow a=\frac{9.10^2}{5.70} \\ \Rightarrow a=\frac{14.52m}{s^2} \end{gathered}[/tex]The acceleration is:
[tex]a=14.52m/s^2[/tex]Car A starts from rest at t =0 and travels along a
straight road with a constant acceleration of 2 ft/s^2 of until it
reaches a speed of 74 ft/s^2 . Afterwards it maintains this
speed. Also, when t = 0 , car B located 5760 ft down the
road is traveling towards A at a constant speed of 56 ft/s^2 .
Determine the distance traveled by car A when they pass
each other.
The distance traveled by car A when they pass each other is 3278.2 ft.
What is the time taken for the two cars to meet each other?The time taken for the two cars to meet each other is calculated by applying the concept of relative velocity.
(Va + Vb)t = d
where;
Va is the velocity of car AVb is the velocity of car Bt is the time of motion of the two carsd is the distance between the cars(74 + 56)t = 5760
130t = 5760
t = 5760/130
t = 44.3 s
The distance traveled by car A when they pass each other is calculated as follows;
da = 74 ft/s x 44.3 s
da = 3,278.2 ft
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alena is performing a floor routine. in a tumbling run she spins through the air, increasing her angular velocity from 43.00 to6 5.00 rev/s while rotating through one-half of a revolution. how much time does this maneuver take?
The tumbling run by Alena lasted for 0.009 seconds.
The time of tumbling can be calculated using the formula -
time = (2 × theta) ÷ (initial angular velocity + final angular velocity)
Keep the values in formula to find the amount of time took while tumbling.
Time = (2 × 0.5) ÷ (43 + 65)
Performing multiplication in numerator and addition in denominator of Right Hand Side of the equation
Time = 1 ÷ 108
Performing division on Right Hand Side of the equation
Time = 0.009 seconds
Thus, Alena took 0.009 seconds in tumbling while performing floor routine.
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Explain some endless capabilities of our vast universe?
ANSWER:
STEP-BY-STEP EXPLANATION:
Answer:
It is impossible to answer that as we could discover more than we know now in years to come with advanced technologies
Explanation:
the chemical makeup of a star's surface is obtained by ... a. examining rocks recovered from the moon. b. examining rocks here on earth. c. examining material collecting on solar panels here on earth.
option c is the correct answer
What is Spectroscopy ?
It is a common method used by astronomers to determine the composition of stars, planets, and other objects. Today, this process uses instruments with gratings that distribute the light from the object by wavelength. This spread of light is called the spectrum.
The science of spectroscopy is very difficult. From the spectral lines, astronomers can not only determine the element, but also the temperature and density of this element within the star. The spectral lines also tell us about each of the star's magnetic fields. The width of the line tells us how fast the matter is moving.
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What will be the next step in our sun's life cycle?A. white dwarf B. red giantC. supernovaD. black hole
ANSWER:
B. red giant
STEP-BY-STEP EXPLANATION:
The Sun is currently a main sequence star and will remain so for another 5 billion years. It will then expand and cool down to become a red giant, after which it will contract and heat up again to become a white dwarf.
Therefore, the correct answer is: B. red giant
in the video, forces acting on the car that are parallel to the direction of motion are analyzed. how are these forces related?in the video, forces acting on the car that are parallel to the direction of motion are analyzed. how are these forces related?
The forces have a same magnitude, act in opposing directions, and result in a net force of zero. The forces produce a net force in the direction of motion that is in the same direction, but they are not equal in size.
All forces operating on an automobile travelling uniformly at a steady speed are balanced. In this instance, the two opposing forces air resistance and friction perfectly balance the force that the wheels are exerting on the ground. However, the instant your foot leaves the gas pedal, there is no longer an applied force, and the forces are out of balance: Now when the car is out of balance, the forces pushing backward on it cause it to slow down; this is known as negative acceleration.
Because there wasn't enough upward force (i.e., regular force from the chair) to balance the extra mass, you would speed downward as a result of the unbalanced force, possibly breaking your tailbone as you plunged through the chair to the floor.
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Cocoa is made from _______. a. cacao beans b. cacao leaves c. the meat of the cacao fruit d. milk, butter, sugar and cacao fruit please select the best answer from the choices provided a b c d
The correct option is (a) Cocoa beans are used to make cocoa.
Cocoa bean shapes during manufacture The dried and fully fermented seed of Theobroma cacao, usually known as the cocoa bean or simply cocoa, is where cocoa solids and cocoa butter are extracted.
The dried, fully fermented cacao grain known as Theobroma is what is commonly referred to as a cacao bean or a cocoa bean. Solids, a mixture of nonfat substances, and cocoa butter, or lard, can be extracted from Theobroma cacao. The chocolate and meals from Mesoamerica were made from these cacao beans. As a result, cacao beans are used to create chocolate.
Hence, cocoa is made from cocoa beans.
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A bus traveling at a speed of 50 km/h has a momentum of 180,345
kg.m/s. What is the mass of the bus?
The mass of the truck is 12,974.4kg .
Describe bulk in plain terms.As a measure of inertia, which is a fundamental characteristic of all matter, mass is used in physics. Effectively, it is the resistance a body of matter offers to a change in its speed or position as a result of the application of a force.
An object's mass is what?Measures a substance's resistance to acceleration in physics. A measure of an object's mass is roughly equivalent to counting the atoms that make up the object. The kilogram serves as the fundamental mass unit. Mass multiplied by the gravitational acceleration equals weight.
50km/h =50×5/18 m/s= 13.88 = 13.9
momentum (p)=180,345 kg.m/s
P=mv
180,345= m X 13.9
m = 180345/13.9
m = 12,974.46
m = 12,974.4
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HELP ASAP!!
What has more momentum in a collision, a fly or a Corvette?
According to Newton’s third law, the force of a fly on the windshield of a Corvette is equal to the force of the Corvette’s windshield on the fly, only in the opposite direction. Why then does the fly get crushed and the Corvette doesn't even feel the collision? This is where momentum comes into play. Momentum of an object is its mass in kilograms times its velocity in m/s. The mass of the fly is 0.2 kilograms and it’s flying at a velocity of 11 meters per second. The Corvette has a mass of 1,518 kilograms and is driving with a velocity of 27 m/s in the opposite direction. During the collision, the Corvette’s mass times velocity will equal a greater momentum because it has significantly more mass and a much greater velocity than the fly.
ANSWER BELOW USING THE RACES STRATEGY
Answer:
convert not telling why but it was the answer I gave it says it was right
Momentum of an object is directly proportional to the mass of the object. The corvette has greater mass and thus more momentum it gains than the little fly.
What is momentum:Momentum of an object is the product of mass and velocity. Thus momentum is directly proportional to the mass and velocity of the object. This relation of momentum with mass and velocity is defined by Newton's law of motion.
According to Newton's third law of motion every reaction has an equal and opposite reaction. Thus if apply a force on object it may return a force but that will depend on the mass and direction.
When the fly hit the moving corvette, the greater impulse will be for the fly since it is very less in mass compared to that of the corvette. The momentum of corvette is higher because velocity and mass of the corvette is significantly higher than that of fly.
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A cosmic-ray electron moves at 7. 5 × 10^6 m/s perpendicular to earth’s magnetic field at an altitude where the field strength is 1. 0 × 10^-5t. What is the radius of the circular path the electron follows?.
4.266 m is the radius of the circular path the electron follows
Electron's speed = 7.50 × 10⁶ m/s
Magnetic field, B = 1 × 10⁻⁵ T
Electron's mass. m = 9.11 × 10⁻³¹
Charge of electron, q = 1.6 × 10⁻¹⁹
We know the relation of radius of curvature, = 4.266 m
What is a circle's radius of curvature?Every point on a circle has a curvature that is equal to the reciprocal of the radius; for other curves (and straight lines, which can be thought of as circles of infinite radius), the curvature is equal to the reciprocal of the radius of the circle that at that point most closely approximates the curve.
The curvature's reciprocal, R, is the radius of curvature in differential geometry. It is equal to the radius of the circular arc that, at that moment, most closely resembles the curve for a curve. The radius of curvature for surfaces is the diameter of a circle that, individually or in combination, best fits a normal section.
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Figure 5 shows a ray of light in an optical fibre.
Figure 5
Inside of optical fibre
What is the name given to the dotted line on Figure 5?
[1 mark]
The technology that sends information as light pulses via a glass or plastic fiber is known as fiber optics, or optical fiber. These glass fibers can range in quantity from a few to several hundred in a fiber optic cable. The glass fiber core is encircled by yet another glass layer known as cladding.
What fiber optics does and how it works?In fiber optics, data is sent as pulses of light, or photons, that travel over a fiber optic cable. Incoming light is bent at a specific angle due to the differing refractive indices of the glass fiber core and cladding.
Total internal reflection is the method by which light signals traveling through fiber optic cable bounce off the core and cladding in a series of zigzag motions. Due to the thick glass layers, the light signals move around 30% slower than the speed of light instead of at the speed of light.
Fiber optic transmission sometimes needs repeaters at a distance to renew, or amplify, the signal throughout its path. By converting the optical signal to an electrical signal, processing that electrical signal, and then retransmitting the optical signal, these repeaters regenerate the optical signal.
Up to 10 Gbps transmissions can currently be supported by fiber optic connections. A fiber optic cable often gets more expensive as its bandwidth capacity increases.
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Select the correct answer from each drop-down menu. earth's rotation causes the cycle of . if earth began to spin a little bit faster .
a 7.50-nc point charge is located 1.80 m from a 4.20-nc point charge. (a) find the magnitude of the electric force that one particle exerts on the other. (b) is the force attractive or repulsive?
The electric force is 8.370 x 10^9N.
We need to know about the electric force to solve this problem. The electric force produced by charges interacting each other, whose strength is given by the equation
F = k.Q1 . Q2/r²
where F is the electric force, Q1 and Q2 is the charge and r is the radius.
From the question above, we know that
k = 9 x 10⁹ Nm²/C²
Q1 =e = 7.50 x 10^-9 C
Q2 = e = 4.02 x 10^-9 C
r = 1.80 m
The electric force will attract each other when the charges are different and will repel each other when the charges are same.
F = k.Q1 . Q2/r²
F = 9 x 10⁹ . 7.50 x 10^-9 . 4.02 x 10^-9/(1.80)²
F = 8.37 x 10^9 N
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You are driving at the speed of 29.5 m/s
(66.0037 mph) when suddenly the car in
front of you (previously traveling at the same
speed) brakes and begins to slow down with
the largest deceleration possible without skidding. Considering an average human reaction,
you press your brakes 0.558 s later. You also
brake and decelerate as rapidly as possible
without skidding. Assume that the coefficient
of static friction is 0.708 between both cars’
wheels and the road.
The acceleration of gravity is 9.8 m/s
2
.
Calculate the acceleration of the car in front
of you when it brakes.
Answer in units of m/s
2
.
The acceleration of the car in front before stopping is 6.94 m/s².
What is the acceleration of the car?The acceleration of the car is the rate of change of velocity of the car with time.
The acceleration of the car in front is determined by applying the Newton's second law of motion assuming the car decelerated at a constant rate before stopping.
Ff = F
μmg = ma
μg = a
where;
Ff is the frictional force on the car when it stopsF is the force of the carm is the mass of the cara is the acceleration of the carg is acceleration due to gravityμ is coefficient of static frictionSubstitute the given parameters and solve for the acceleration of the car.
a = (0.708) x (9.8 m/s²)
a = 6.94 m/s²
Thus, the acceleration of the car in front before stopping is 6.94 m/s².
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How are an electromagnetic wave’s wavelength and frequency related to the wave’s period of oscillation?.
If air resistance can be neglected, what happens to the horizontal velocity
of a basketball as it is thrown to the basket from the free-throw line?
O decreases
O stays constant
O increases
increases while the ball is going up, and then decreases while the ball is coming
down
O decreases while the ball is going up, and then increases while the ball is coming
down
If air resistance can be neglected, what happens to the horizontal velocity of a basketball as it is thrown to the basket from the free-throw line increases while the ball is going up, and then decreases while the ball is coming down.
Does the horizontal velocity change if air resistance is neglected?- When anything is hurled horizontally, gravity accelerates the object downward. – The only direction in which gravitational acceleration occurs is vertical. If we exclude the effects of air resistance, the object's horizontal velocity remains constant.
We know that the horizontal component of the force acting on the projectile at any given time will be zero if the air resistance is ignored in the projectile motion, which results in Fx=0.
The only force operating on the body in a horizontal direction if we neglect air resistance is gravity, which is acting in a vertical direction. As a result, the horizontal motion moves at a constant speed.
Therefore, option C is correct.
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what is the momentum of an 7.2- kg bowling ball rolling at 3.0 m/sm/s ? express your answer to two significant figures and include the appropriate units.
The momentum of an 7.2 kg bowling ball rolling at 3 m/s is 21.6 kgm/s.
What is momentum and how the momentum of bowling ball calculated out to be 21.6 kgms?Momentum is defined simply as the quantity of motion of the body , but it is the product of mass and velocity.There are several kind of momentum like linear momentum, translational momentum.Here is given the mass of the object 7.2 kg and the velocity is 3 m/s of the ball.Now to calculate the momentum we will simply apply the formula momentum = mass x velocity.7.2 x 3 = 21.6 kg-m/s is the momentum of the bowling ball rolling at 3 m/s .To know more about momentum visit:
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PLEASE ANSWER ASAP!
On average, there is enough wind in the UK each year to supply all of the UK's electricity needs.
Explain why the UK may still need power stations that use fuel to generate electricity.
(2 marks)
Explanation:
Unplanned maintenance at nuclear plants and lower than average wind speeds mean the country is currently relying on gas-powered stations to generate about half its electricity
The UK depends on power stations due to the more efficiency of energy production in them.
Even though UK has an enough wind supply over each year to meet the electric needs of UK, they still need power stations that use fuel to generate electricity.
This is because of the challenges created in the maintenance and implementation of wind plants in the UK.
The wind turbines have a higher cost for maintenance, compared to that of power stations. The ideal wind sites in the UK are mostly located in remote areas, so that it becomes more difficult for the implementation of wind plants. Also the lower average wind speed causes less production in the electricity through them. As a result, the UK still depends on power stations for the electric needs.
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While traveling, an airplane passenger placed a bag of potato chips in his checked luggage that was placed in the baggage compartment where the air was not regulated. When he opened the luggage after landing, the bag had exploded and potato chips were everywhere in his luggage. Which gas law does this describe?.
While traveling, an airplane passenger placed a bag of potato chips in his checked luggage that was placed in the baggage compartment where the air was not regulated. When he opened the luggage after landing, the bag exploded and potato chips were everywhere in his luggage. Boyle's law explains this phenomenon.
According to Boyle's law, the volume of a gas and its pressure are inversely proportional to each other.
In a bag of potato chips, nitrogen gas is filled to prevent breakage and keep the flavor intact.
At Earth, the pressure of the gas inside the package is less than the surrounding pressure and it prevents the potato pouch from bloating up. However, at higher altitudes, pressure decreases, and the volume of the gases inside the bag expands under lower pressure and ultimately the bag explodes.
In general, when the pressure of the potato bag becomes greater than the surrounding pressure, then it explodes.
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an old chrysler with mass 2050 kg is moving along a straight stretch of road at 75 km/h. it is followed by a ford with mass 1300 kg moving at 40 km/h. how fast is the center of mass of the two cars moving?
the center of mass of the two cars moving is with a speed of 61.41m/s
What is center of mass ?
A position established in relation to an object or set of objects is the center of mass. It represents the system's average location as weighted by each component's mass. The centre of mass for straightforward stiff objects with homogeneous density is found at the centroid.
The center of mass also functions as a location at which inertial forces, such as centrifugal force, and gravitational force are applied. There are a number of direct and indirect techniques for locating the center of mass.
Let mc be the mass of the Chrysler and νc be its velocity .
Let mf be the mass of the Ford and νf be its velocity . Then the velocity of the center of mass is
ν com = (mc v c + mf v f) /m c+ m f = [tex](2050*75 + 1300*40)/(2050+1300)[/tex]
= 61.41 km/h
We note that the two velocities are in the same direction, so the two terms in the numerator have the same sign.
the center of mass of the two cars moving is with a speed of 61.41m/s
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what is the name of the theory that describes the history and fate of the universe?? what is the name of the theory that describes the history and fate of the universe?? the nebular theory. the big bang theory. the theory of everything. the general theory of relativity.
The name of the theory that describes the history and fate of the universe is the big bang theory.
The most influential theory of the origin of the universe at present is the so-called Big Bang theory. According to this theory, the universe was formed when a very hot dense fireball exploded, blowing matter outward. The consensus among scientists, astronomers, and cosmologists is the universe as we know it.
It was created in a massive explosion that determined not only most of the matter but also the physical laws that govern our ever-expanding universe about it. This is known as the Big Bang Theory. The most widely held theory of the origin of the universe is called the Big Bang theory. This argues that the universe began as a near-single point with near-infinite temperature and density. Since then the universe has continued to expand.
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Physics Trajectory question.
I need help finding the answers on Vy.
The vertical component of the velocity after the given interval of time will be:
B: -9.8 m/s
D: -19.6 m/s
F: -29.4 m/s
H: -39.2 m/s
What is a projectile?A projectile can be described as any object upon which the only force is gravity. The projectile travels with a parabolic trajectory because of the influence of gravity. No horizontal forces are acting upon projectiles so there is no horizontal acceleration.
The horizontal velocity of a projectile is constant and the vertical acceleration is caused by gravity. The vertical component of the velocity of a projectile changes by 9.8 m/s each second while the horizontal motion of a projectile is independent of its vertical motion.
Given, the initial horizontal velocity, vₓ = 18 m/s
The initial vertical velocity, Vy = 0 m/s
The time interval = 1 sec
The vertical component of the velocity is calculated as;
[tex]V_y = V_{0y} -gt[/tex]
[tex]V_y = 0- (9.8) (1)\\V_y = -9.8 m/s[/tex]
The vertical component when t = 2 sec and horizontal velocity, Vx = 18 m/s
[tex]V_y = 0- (9.8) (2)\\V_y = -19.6 m/s[/tex]
The vertical component of velocity when t = 3sec:
[tex]V_y = 0- (9.8) (3)\\V_y = -29.4 m/s[/tex]
The vertical component of velocity when t = 4sec:
[tex]V_y = 0- (9.8) (4)\\V_y = -39.2 m/s[/tex]
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The velocity of a wagon increases from 3 m/s to 9 m/s as it
accelerates uniformly down a hill. The average velocity of the
wagon is
m/s.
Answer:
6 m/s
Explanation:
The equation that relates time, distance, and acceleration is:
a = (vf - vi)/t
where a is acceleration (m/s^2), time is time (seconds) and vf and vi are the initial (vi) and final (vf) velocities (m/s).
Average velocity is (vf + vi)/2
We are given that:
vi = 3 m/s
vf = 9 m/s
Average velocity for the wagon is thus:
is (9 + 3)/2 = 6 m/s
If the same elevator accelerates downwards
with an acceleration of 1.2 m/s
2
, what is the
upward force exerted by the elevator floor on
the passenger?
The upward force exerted by the elevator floor on the passenger is 7.6 times mass of the passenger.
What is force?A force in physics is an effect that has the power to alter an object's motion. 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.
Given in question elevator accelerates downwards with an acceleration of 1.2 m/s². There is acceleration due to gravity working downward which is 9.8 m/s².
So, net acceleration due to gravity is given as 9.8 - 1.2 = 7.6 m/s²
The upward force exerted by the elevator floor on the passenger is mass times acceleration, 7.6 times mass of passenger.
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If Earth's circumference at the
equator is 40,070 km, what is the
speed of the stationary satellite
GOES above the equator in km/
hour? (Use the formula: Speed =
Distance/Time)
The stationary satellite crosses the equator at a speed of 1180 kilometres per hour.
How does speed at the equator get calculated?At the equator, where the Earth's circumference is 40,070 kilometres and the day lasts for 24 hours, the speed is 1670 kilometres per hour (1037 miles per hour). This slows down by the latitude's cosine, so at a latitude of 45 degrees, cos(45) =. 707, and the speed is. 707 x 1670 = 1180 kilometres per hour.
How fast would a student travelling at the equator while seated on Earth's surface?
The daily motion felt on our earth is brought on by this spinning. You would move at almost 1,000 miles per hour (1,600 km/hr) if you were standing on the equator of the Earth, but your pace would slow down if you started moving in the direction of the North or South Poles.
A latitude of 45 degrees, cos(45) =. 707, and the speed is. 707 x 1670 = 1180 kilometres per hour.
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A vector has an x-component of length 3 and a y-component of length 4 what is the angle of the vector
The angle of a vector with x and y component of 3 and 4 respectively is 53.13°
What is a vector?
Vectors are quantities that have both magnitude and direction
To calculate the angle of the vector, we use the formula below.
Formula:
∅ = tan⁻¹(y/x)........... Equation 1Where:
∅ = Angle of the vectorx = x-component = 3y = y-component = 4Substitute these values into equation 1
∅ = tan⁻¹(4/3)∅ = tan⁻¹(1.33)∅ = 53.13°Hence, the angle of the vector is 53.13°.
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a boy and a girl are at rest on separate skis 12 m apart on a horizontal icy surface. the boy and his skis have twice the inertia of the girl and her skis. determine the location of the center of mass in meters measured from the position of the girl.
With the position of the girl as a reference point, the center of mass is 8 m from the girl position.
If there are two objects as shown on the attached picture, the center of mass is:
xc = m₁ / (m₁ + m₂) . x₁ + m₂ / (m₁ + m₂) . x₂
From the problem, we know that the boy and his skis have twice the inertia of the girl and her skis. We can replace the mass in the equation with inertia, hence:
xc = I₁ / (I₁ + I₂) . x₁ + I₂ / (I₁ + I₂) . x₂
Let:
I₁ = the girl's inertia
I₂ = the boy's inertia
Hence,
I₂ = 2 I₁
Let make the position of the girl as a reference point, then,
x₁ = 0
x₂ = 12
Plug these parameters into the formula:
xc = I₁ / (I₁ + I₂) . 0 + 2 I₁ / (I₁ + 2 I₁) . 12
xc = 2/3 . 12 = 8 m
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