The magnitude is 4.1.
What is the magnitude of the vector?We must know that a vector is a quantity that has both magnitude and direction. The term magnitude refers to the amount of the vector while the direction shows the place where the vector is headed. It is common to write a vector in bold face or to show the direction of the vector by use of an arrow written above the symbol of the vector.
In this case, we have vector that is shown in the given directions and we have been asked to find the magnitude of the vector. We could find the magnitude of the vector from; √(1)^2 + (4)^2 = 4.1
Thus, the magnitude is 4.1.
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A 1.5 kg mass swings at the end of a 2.3 m string. A scale on the string
measures the tension in the string to be 24.5 N. What is the centripetal
force on the swinging mass? __________ Blank 1
And, what is the speed of the mass at the time the tension is measured?
The speed of the mass at the time the tension is measured is 6.12m/s
centripetal force - It is a force which makes a body follow a curved path.
It is directed inward towards center of rotation.
for example - gravitational force of sun is a centripetal force that keeps earth rotating around it.
the centripetal force on the swinging mass
Fc = mv²/r
where Fc is the centripetal force
m is the mass of body
v is the velocity
r is the radius
m = 1.5
r = 2.3 m
F = 24.5 N
To calculate the speed we put values in above equation
Fc = mv²/r
v = sqrt(Fc x r / m)
v = [tex]\sqrt[]{\frac{F *m}{r} }[/tex]
[tex]v = \sqrt[]{\frac{24.5*1.5}{2.3} }[/tex]
v = 6.12m/s
The speed of the mass at the time the tension is measured is 6.12m/s
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Describe the mechanism that orchids use to control their pollen distribution.
The pollination methods used by orchid plants to control their pollen distribution include:
Use of nectar rewards use of deceptionUse of trapsWhat is pollination?Pollination is the process by which pollen grains are transferred from the anther to the stigma of the flowers of the same plant or another plant.
When pollination occurs in the same flower of the same plant, it is know as self-pollination.
When pollination occurs in the different flowers of the same or different plants, it is know as cross-pollination.
Considering the orchid plants, the methods which they employ to control their pollen distribution is as follows:
Use of nectar rewards -some orchids attract their pollinators with reward of nectaruse of deception: some orchid species attract their pollinators by means looking like their mating partners making them to think they are mating partnersUse of traps - some orchids use traps to get their pollinators to pollinate them.Learn more about pollination at: https://brainly.com/question/23540386
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A piolet is required to fly directly from London,United Kingdom, to Rome,Italy,in 3.4 h. The displacements is 1.4×10³km[S 43⁰ E] . The wind velocity reported from the ground is 55km/h[S]. Determine the required velocity of the plane relative to the air.
The required velocity of the plane relative to air with a velocity of 55 km / h S is 373.42 km / h
v = d / t
d = 1400 km ( 43° E of S )
t = 3.4 hrs
[tex]V_{pg}[/tex] = d / t
[tex]V_{pg}[/tex] = 1400 / 3.4
[tex]V_{pg}[/tex] = 411.75 km / h ( SE )
[tex]V_{ag}[/tex] = 55 km / h ( S )
[tex]V_{pgx}[/tex] = sin 43° ( 411.75 )
[tex]V_{pgx}[/tex] = 280.81 km / h ( E )
[tex]V_{pgy}[/tex] = cos 43° ( 411.75 )
[tex]V_{pgy}[/tex] = 301.14 km / h ( S )
[tex]V_{x}[/tex] = [tex]V_{pgx}[/tex] - [tex]V_{agx}[/tex]
[tex]V_{x}[/tex] = 280.81 - 0
[tex]V_{x}[/tex] = 280.81 km/ h
[tex]V_{y}[/tex] = [tex]V_{pgy}[/tex] - [tex]V_{agy}[/tex]
[tex]V_{y}[/tex] = 301.14 - 55
[tex]V_{y}[/tex] = 246.14 km / h
V² = [tex]V_{x}[/tex]² + [tex]V_{y}[/tex]²
V = √ [ ( 280.81 )² + ( 246.14 )² ]
V = 373.42 km / h
tan θ = [tex]V_{y}[/tex] / [tex]V_{x}[/tex]
θ = [tex]tan^{-1}[/tex] ( 246.14 / 280.81 )
θ = [tex]tan^{-1}[/tex] ( 0.88 )
θ = 41.35° ( S of E )
Therefore, the required velocity of the plane relative to air is 373.42 km / h at 41.35 S of E
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The Distance-time graph shown is for a 3000 m cross-counrty race, run by rachel and james.
From the given graph, it is shown that James is running the race with the same speed while Rachel changes his speed time-to-time. It can be inferred from the graph that James wins the race.
What is Speed?Speed is the distance travelled by an object in a particular time. In the race, James run with a constant speed throughout the race and Rachel changes its speed after some time.
By looking at the graph, we can say that James catch up Rachel 17.5 minutes after the start of the race where they both completed 1750m distance.
Speed of James can be calculated by the formula:
Speed = Distance/Time
Speed = 3000m/30min
Speed of James = 100m/min.
Different speeds of Rachel can be calculated by the same formula:
For the first 1000m he completes the distance in 5 min. therefore, the speed will be:
Speed = 1000m/5min.
Speed = 200m/min.
For the next 1500m. he covers the distance in 25min. therefore, the speed here will be:
Speed = 1500m/25min.
Speed = 60m/min.
For the next 500m. he covers the distance in 5 min. therefore, the speed will be:
Speed = 500m/5min.
Speed= 100m/min.
As, James covers the same distance earlier than Rachel. James cover the the distance in 30 minutes while Rachel covers the same distance in 35 minutes. James will be the winner of the race.
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A record of travel along a straight path is as follows:
1. Start from rest with constant acceleration of 2.25 m/s2 for 19.0 s.
2. Maintain a constant velocity for the next 2.50 min.
3. Apply a constant negative acceleration of −9.09 m/s2 for 4.70 s.
(a) What was the total displacement for the trip? m
(b) What were the average speeds for legs 1, 2, and 3 of the trip, as well as for the complete trip?
leg 1 m/s
leg 2 m/s
leg 3 m/s
complete trip m/s
The total displacement is 4317.34 meters and the average speeds of the legs are 27.36m, 54.72m, 27.35m.
What is average speed?The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
a = 2.25 m/s2 ; t1 = 19 s ; t = 2.50 min = 150 sec ; a' = -9.09 m/s2 t3 = 4.70 s
(a)The velocity at the end of the first interval will be given by
V = u + at = 0 + a t1 = 2.25 x 19 = 42.75 m/s
This velocity will remain the same throughout the second period in accordance with point (2) and serve as the initial velocity for the third interval.
We now see that, if s is the displacement, s = u t + 1/2 a t2
In our situation, the sum of the displacements in the specified three intervals will represent the total displacement.
[tex]\Delta s(total) = \Deltas1 + \Deltas2 + \Deltas3[/tex]
[tex]\Delta s(total) = [0 + 1/2 x 2.88 x (19)2) + [54.72 x 66 + 0] + ( 54.72 x 6.8 + 1/2 x (-8.05) x (6.8)2][/tex]
[tex]\Delta s(total) = 519.84 + 3611.52 + 185.98 = 4317.34 meters[/tex]
Hence,
[tex]\Delta s(total) = 4317.34 meters = 4.32 Km.[/tex]
(b)Speed for leg 1 will be
v1 = [tex]\Delta s1 / t1 = 519.84 / 19 = 27.36 m/s[/tex]
Speed for leg 2 will be
[tex]v2 = \Delta s2 / t2 = 3611.52 / 66 = 54.72 m/s[/tex]
Speed for leg 3 will be
[tex]v2 = \Delta s3 / t3 = 3611.52 / 66 = 185.98 / 6.8 = 27.35 m/s[/tex]
The average velocity of the complete trip will be given as follows:
V = [tex]\Delta s(total) / t(total)[/tex]
t(total) = t1 + t2 + t3 = 19 + 66 + 6.8 = 91.8 s
[tex]V = \Delta s(total) / t(total) = 4317.34 meters / 91.8 = 47.03 m/s[/tex]
Hence, V = 47.03 m/s
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In which of the following situations are you doing positive work on the box?
Throwing a box at someone.
Carrying a box in your arms across the room.
Carrying a box in your arms up the stairs.
Holding a box in your out-stretched arms, spinning around in a circle.
Catching a box that is thrown at you.
Pushing a box on the floor across the room.
Carrying a box in your arms down the stairs.
Holding a box in your arms.
F. The situation in which the work done is positive is, "Pushing a box on the floor across the room.".
What is positive work?The work done on an object is said to be positive work when force applied on the object causes a displacement of the object in the same direction.
Some of the examples of positive work include the following:
pushing a table or chair across a horizontal surfacePushing a box on the floor across the room.From the given options, the only option in which the applied force is in the same direction as the box's displacement is option F "Pushing a box on the floor across the room".
Thus, the situation in which the work done is positive is, "Pushing a box on the floor across the room.".
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how does mass and velocity determine the amount of damage that occurs in a collision?
Answer:
Mass and velocity are both directly proportional to the momentum. If you increase either mass or velocity, the momentum of the object increases proportionally. If you double the mass or velocity you double the momentum.
Explanation:
John is traveling north at 20 meters/second and his friend Betty is traveling south at 20 meters/second. If north is the positive direction, what are John and Betty's speeds?
A.
-20 meters/second, 20 meters/second
B.
20 meters/second, -20 meters/second
C.
-20 meters/second, -20 meters/second
D.
0 meters/second, 40 meters/second
Answer:
B. 20 meters/ second, -20 meters/ second
define physical fitness in your own definition
"One's capacity to carry out daily activities with maximum efficiency, strength, and endurance while managing the illness, exhaustion, and stress and engaging in less sedentary behavior."
The health of the heart, lungs, and muscles is a component of physical fitness. Fitness also somewhat affects traits like mental acuity and emotional stability because what we do with our body also affects what we can do with our minds.
Hence Being physically fit doesn't need include dominating a particular sport or having bulging muscles.
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Which of the following best describes the difference between experiments and correlational research methods? Which of the following best describes the difference between experiments and correlational research methods? Experiments use one type of statistical test; correlational methods use a different type of statistical test Experiments allow researchers to make claims about one thing causing the other; correlational methods don't Experiments are always the best form of research to do; correlational methods are inherently worse
(A) Experiments use one type of statistical test; correlational methods use a different type of statistical test
Correlational research:
A non-experimental research method known as correlational analysis measures two variables and evaluates the statistical relationship (also known as the correlation) between them with little to no effort to control unrelated variables. There are a variety of factors to consider when deciding whether to perform an experiment or a correlational study by researchers interested in statistical correlations between variables. First off, they either don't think the statistical relationship is causative or aren't interested in causality. Remember that the two main objectives of science are to describe and predict; the correlational research approach enables researchers to accomplish both of these objectives.Experimental research:
Experimental research is a term used to describe a study that closely resembles a scientific research methodology. A hypothesis, a controlled variable, and variables that can be measured, computed, and compared make up this structure.The utilization of controlled conditions in experimental research is vital. The facts that the researcher gathers will either confirm or disprove the theory.Difference between experimental and correlational methods:
You alter an independent variable and track its impact on a dependent variable in an experimental design. Other factors cannot affect the outcomes because they are under control. You measure variables in a correlational design without changing any of them.
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What is the first step to composing a short piece?
A. Choosing an image as stimuli
B. Choosing your lyrics
C. Choosing a rhythm and a melody
Which variable represents displacement?
Question 5 options:
t
a
v
d
The variable that represents displacement is "d" (option D).
What is displacement?Displacement in physics is a vector quantity which denotes distance with a directional component.
Displacement, unlike distance is a vector quantity i.e. it has magnitude and direction.
Displacement is the measure of “how far out of place is an object. The distance of a body can be denoted by "d".
The displacement of a body can be calculated as follows:
∆d = x¹ - x²
Where;
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6) A person on a bus traveling 5 m/s is walking to the back of the bus at 1 m/s. How fast does
the person on the bus appear to be moving to a person in a car going the opposite direction
traveling at 2 m/s?
Answer:
maximum velocity,then u draw your diagram then u calculate for max velocity then the answer u get use it for total shape
Can someone solve this problem thank you!
(a) Capacitance = 4.43 * 10⁻¹¹ F
(b) Magnitude of the charge on each plate = 2.9238 * 10⁻⁸ C
(c) Stored Energy = 8.7714 * 10⁻⁶
(d) The electric field between the plates = 6.0 * 10⁴ V/m
(e) The energy density between the plates = 1.45 J/m³
(A) The ability of a conductor or group of conductors to store a separated electric charge for a given change in electrical potential is known as its capacitance. The term "capacitance" also suggests the storage of electrical energy.
Capacitance (C) = A∈ / d = [tex]\frac{55 * 10^{-4}* 8.86 * 10^{-12}}{0.011}[/tex] = 4.43 * 10⁻¹¹ F
Therefore, Capacitance = 4.43 * 10⁻¹¹ F
(B) The force per charge on any particular test charge situated within the electric field is used to calculate the electric field vector's magnitude. Either the source charge or the test charge could be directly affected by the force acting on it.
The magnitude of the charge on each plate (Q) = CV
Q = 4.43 * 10⁻¹¹ * 660 = 2.9238 * 10⁻⁸ C
Therefore, the magnitude of the charge on each plate = 2.9238 * 10⁻⁸ C
(C) The energy that a thing retains due to its position in relation to other objects, internal tensions, electric charge, or other causes is known as stored energy.
Stored Energy (U) = 0.5 CV² = 8.7714 * 10⁻⁶ J
Therefore, Stored Energy = 8.7714 * 10⁻⁶ J
(D) The region or place where the influences of the plates' charges are visible is the electric field between the plates. For instance, any charged plate will produce an electric force to either attract or repel a charged particle if it is placed close to it.
The electric field between the plates (E) = V / d = 660 / 0.011 = 6 * 10⁴ V/m
Therefore, The electric field between the plates = 6.0 * 10⁴ V/m
(E) The quantity of energy that can be held in a specific system, substance, or area of space is known as its energy density. Energy per volume or mass can be used to measure energy density. A system or material has more energy stored in it when its energy density is higher.
The energy density between the plates (u) = U / Ad = [tex]\frac{8.7714 * 10^{-6} }{(55 * 10^{-4}) (1.1 * 10^{-3})} = \frac{0.0000063}{0.0055 * 0.0011} = \frac{0.00000878}{0.00000605} = \frac{878}{605} = 1.45 Jm^{3}[/tex]
Therefore, The energy density between the plates = 1.45 J/m³
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Dean is slowing down on his skateboards. He starts at a speed of 5.5 m/s and
slows to 1.0 m/s over a time of 3.0 seconds. What is Dean's acceleration?
Dean's acceleration while slowing down on his skateboards a = -1.5 m/s².
Equation :To find the acceleration of skateboards
Using formula,
a = Δv/Δt
where,
a is acceleration
Δv is change in speed
Δt is time
By putting the given values,
a = 1.0 m/s - 5.5 m/s / 3 s
a = - 4.5 m/s / 3s
a = -1.5 m/s²
Is acceleration can be positive or negative?When an object is moving in a positive direction, the acceleration is negative, but the rate of change of velocity is positive (velocity is decreasing). When an object moves in the reverse or opposite direction, we can define these two accelerations as well (right to left).
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Why does gravity cause acceleration?
Answer choices
A. It acts in a downward direction
B. It has a greater effect on objects with more mass.
C. It always causes objects to slow down.
D. It is a force.
The following graph illustrates how jamil moves as he goes to the paper shop
The graph is the visual representation of information. It shows the information in graphical form.
What is a graph?The graph shows a visual representation of information.
(a) It will take 360 seconds to travel to the shop.
(b) Jamil covers 400 + 90 + 120 km= 610 km distance.
(c) Speed= distance/ time = 610 km/ 360 = 1.69 m/ second.
(d) He spends 360 seconds at the shop.
(e) Speed = d1/t1 + d2/ t2 + d3/ t3= 450/ 150 + 450 / 90 + 450 / 120
= 3 + 5+ 3.75 = 11.75 m / second.
The graph is the visual representation of information. It shows the information in graphical form.
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A car travels on a straight level road. Starting from rest the car is going 32 fr/s (22mi/h) at the end of 4.2s what is the cars average acceleration in ft/s^2
The acceleration of a car that travels on a straight level road starting from rest and going at 32 ft/s at the end of 4.2s is 7.62ft/s².
How to calculate acceleration?The acceleration of a moving car can be calculated by dividing the speed by the time taken as follows:
Acceleration = Speed ÷ time
According to this question, a car travels on a straight level road starting from rest the car is going 32 ft/s (22mi/h) at the end of 4.2s. The acceleration can be calculated as follows:
Acceleration = 32ft/s ÷ 4.2s
Acceleration = 7.62ft/s²
Therefore, the acceleration of a car that travels on a straight level road starting from rest and going at 32 ft/s at the end of 4.2s is 7.62ft/s².
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You push a box down the hallway. The box, with a mass of 30kg, accelerates at a speed of 3m/s2. If the force of friction on the box is 20N, how much did YOU exert in order to move it?
The force you exerted in order to move the box, given the data from the question is 110 N
How to determine the net forceWe'll beging by obtaining the net force on the box. This is illustrated below:
Mass (m) = 30 KgAcceleration (a) = 3 m/s²Net force (Fn) =?Net force = mass × acceleration
Net force = 30 × 3
Net force = 90 N
How to determine the force exertedFinally, shall obtain the force exerted to the box. This can be obtained as follow:
Net force = 90 NFrictional force = 20 NForce exerted =?Net force = force exerted - frictional force
90 = force exerted - 20
Collect like terms
Force exerted = 90 + 20
Force exerted = 110 N
This, the force exerted on the box is 110 N
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Need help answering this question
Answer:
[tex] log( \beta e \alpha \sin( \cot( \sec( \binom{? \times \frac{ \\ \infty }{?} }{?} ) ) ) ) [/tex]
What is the sum of the following vectors? Write your answer, what magnitude and direction the vector will have?
The magnitude and direction of the object's displacement is 7 m and west direction respectively.
What is displacement?The displacement of an object is the change in the position of the object. Displacement is a vector quantity because it has both magnitude and direction.
To find the sum of the vectors, we find the displacement of the vectors.
Initial position of the vector = 10 m east
final position of the vector = 3 m west
displacement of the vector = final position - initial position
displacement of the vector = 3 m - 10 m
displacement of the vector = - 7 m
magnitude of the displacement = 7 m
direction of the displacement = west
Thus, the magnitude and direction of the object's displacement is 7 m and west direction respectively.
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Which of the following was NOT a part of the arrival process for Jews at the concentration camps?
A. Defense training
B. Losing all possessions
C. Hair shaving
D. Strength test for work
A speedboat with a mass of 531 kg (including the driver) is tethered to a fixed buoy by a strong 30.3 m cable. The boat's owner loves high speed, but does not really want to go anywhere. So the owner revs up the boat's engine, makes a lot of noise, and runs the boat in circles around the buoy with the cable supplying all the necessary centripetal force. When the tension of the cable is steady at 12900 N, with what force is the boat's engine pushing the boat? Different physics textbooks treat drag force somewhat differently and use different formulas. For the present purpose, take the water's drag force on the boat to be (450 kg/m)×2, where denotes the boat's speed. Ignore any drag force on the cable.
As the tension in the rope is constant therefore the boat engine will also be pushing the boat with the same force as that of the drag force that is given to be 450 Newton.
What is a drag force?Drag force is similar to friction force but is experienced by a moving body in a fluid. Direction of drag force is a positive to the direction of motion.
What is centripetal force?Centripetal force is not a new force in nature but a manifestation of some force that causes rotation of a body.
Given:
Mass of the boat = 531 kg
Tension in the cable = 12900 Newton
Drag force experienced by the boat = 450 N
The boat along with the man is rotating using a cable which experiences a constant tension of 12900 Newton.
The boat's engine should also be generating a force perpendicular to the circular path travelled by the boat.
Now the tension in the string is constant this implies that all the force that the both engine is generating is being used in balancing the drag force exerted by water on the boat.
Therefore, the force produced by the engine will be equal to 450 Newton which will be used to balance the drag force.
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By January, the 1.2 kg of water in the birdbath in Robyn’s backyard has frozen to a temperature of -7.6°C. As the season changes, how much heat must be added to the water to make it a comfortable 26.9°C for the birds? Q=mcΔT and Q=mhf
(Heat of fusion for water is 335,000 J/kg) Round to the tenth place.
The heat that is added is 2277 kJ.
What is the heat to be added?We know that heat is a form of energy that appears as a result of temperature difference that exist between two bodies. In this case now, we are told that by January, the 1.2 kg of water in the birdbath in Robyn’s backyard has frozen to a temperature of -7.6°C.
Now there are three transitions that took place here;
The ice was heated to raise its temperature from -7.6°C to zero degreesThe ice melted at zero degreesThe heat required to raise the temperature from zero degrees to 26.9°CThus;
H = mcicedT + mhf + mcwaterdT
H = (1.2 * 2060 * 7.6) + (1.2 * 335,000) + (1.2 * 4182 * 26)
H = 1745kJ + 402 kJ + 130 kJ
H = 2277 kJ
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Science 6a unit 2 test study guide
Please help me out!!! This is a major grade been taking care of my baby brother while mom works barely had time to study!
Answer:
at number 8 the answer is Uranus
Daniel's physician has told him that he needs to spend less time in his office chair because sitting for so long is causing him to have back pain. What ergonomic solution could help him?
(A short explanation is ok if you can)
A) wearing a wrist brace
B) a standing desk
C) moving his monitor closer to his eyes
D) using a speakerphone more often
(please help ill give brainliest as soon as i can =) )
The possible ergonomic solution that could help Daniel reduce hos back pain caused by sitting long on his chair is a standing desk.
What is ergonomic solution?
Ergonomics is defined as the science of creating a working environment that suits the capabilities and limitations of the worker while providing the best working experience.
If Daniel's physician has told him that he needs to spend less time in his office chair because sitting for so long is causing him to have back pain. The possible ergonomic solution that could help him include the following.
Daniel can use a revolving seatDaniel can also use a standing desk; this will enable him stand and reduce his back pain which happens when he sits for long.Thus, the possible ergonomic solution that could help Daniel reduce hos back pain caused by sitting long on his chair is a standing desk.
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Answer: B. A standing desk
Explanation: I remember getting it right on my test.
Think of a pen name that you most likely would use if you are to become a writer. Write it down and give a brief explanation as to why you have chosen that particular pseudonym. Write your explanation on not less that three paragraph with 5 sentence each paragraph
A pen name is the name used by the writer instead of their real name when publishing. This name is called as pseudonym or a fake name. The author's real name is probably known to the publisher, but not to the public.
If I'll be the writer, I'll use Dark Shadow as my pen name.
Dark Shadow effectively acts as a living appendage that obeys his master's every command. It is sentient, capable of speech, and loyally protects its host regardless of its state. Also it is short and sweet name and can be pronounced easily.
Also thee is a drawback in seeking secrecy with the pen name. The Guardian article says, "If you try to keep your identity secret, you can't go to events or festivals; be pictured in newspapers, or be open about your possible success. And, if you become hugely successful, you'll have to come out eventually – as Madeleine Wickham, the author of the Sophie Kinsella books, did. "
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9. The coefficient of static
friction between a 5kg block
and horizontal surface is 0.4.
What is the maximum
horizontal force that can be
applied to the block before it
slips?
Answer:
19.6 Newtons
Explanation:
[tex]\displaystyle \textsf{The weight of the block is W= mg where m is the mass and g the acceleration due to gravity}[/tex]
[tex]\sf W = 5kg, \; and\; g = 9.80 m/s^2[/tex]
[tex]\sf W = 5 x 9.8 = 49\; Newtons[/tex]
[tex]\textsf {If the coefficient of static friction is } $\mu_s$, the force to be applied for the block to slip is given by the equation}:\\\mathsf {f_s = \mu_s \times W}\\\\\textsf {So force required, given $\mu_s$ = 0.4 is: }\\\\\\\mathsf {f_s = 0.4 \times 49 = 19.6 } \textsf{ Newtons }[/tex]
You drive in a straight line at 18.0 m/s for 10.0 mi, then at 30.0 m/s for another 10.0 mi.
You drive in a straight line at 18.0 m/s speed for 10.0 miles, then at 30.0 m/s for another 10.0 miles, then the average speed is calculated as less than 24 m/s. So, the correct option is C.
What is the speed on average?The overall calculated distance that the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
What is a typical speed and an illustration?The entire distance travelled is divided by the time interval to determine average speed.
For instance, someone travelling at an average speed of 40 miles divided by 40 minutes, or 1 mile per minute, is travelling 20 miles north and then 20 miles south (60 mph). Calculating average speed involves dividing the total distance travelled by total time taken.
Here [tex]X_{1}[/tex] = [tex]X_{2}[/tex]
= 10 miles
= 16093.4 m
[tex]t_{1}[/tex] = [tex]X_{1}[/tex]/[tex]V_{1}[/tex]
= 16093.4/18
[tex]t_{1}[/tex]= 894.08s
and then [tex]t_{2}[/tex] = 16093.4/30
[tex]t_{2}[/tex] = 536.45s
Average speed [tex]V_{avg}[/tex] = [tex]\frac{X_{1} + X_{2}}{t_{1} + t_{2} }[/tex]
= [tex]\frac{(16093.4 + 16093.4)}{(894.08 + 536.45)}[/tex]
[tex]V_{avg}[/tex] = 22.50 m/s
Thus, the correct option is that average speed is less than 24 m/s.
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Complete Question
You drive in a straight line at 18.0 m/s for 10.0 miles, then at 30.0 m/s for another 10.0 miles.
Is your average speed
a) 24.0 m/s
b) more than 24.0 m/s
c) less than 24.0 m/s
A ballplayer standing at home plate hits a baseball that is caught by another player at the same height above the ground from which it was hit. The ball is hit with an initial velocity of 26.8 m/s at an angle of 60.0° above the horizontal. At what distance from the home plate will the fielder be when he catches the ball?
The distance from the home plate the fielder will be when he catches the ball is 63.47 m
From the question given above, the following data were obtained:
Initial velocity (u) = 26.8 m/sAngle of projection (θ) = 60.0 °Acceleration due to gravity (g) = 9.8 m/s²Distance (i.e range) (R) =?How to determine the rangeThe distance (i.e range) the fielder will be when he catches the ball can be obtained as follow:
R = u²Sine(2θ) / g
R = 26.8² × Sine (2×60) / 9.8
R = 622.014 / 9.8
R = 63.47 m
Thus, the distance the fielder will be is 63.47 m
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