The average angular speed will be the ratio of total distance to total time which is 5.77 rad/s
What is Angular Speed ?Angular speed can be defined as the total angle turned per total time taken. It is measured in rad/s
Given that a floral clock in Japan has a radius of 15.5 m. If you ride a bike around the clock, making 16 revolutions in 4.5 min, what is your average angular speed ?
The circumference C of the circle = distance covered by the bike.
C = 2πr where r = 15.5 m
C = 2 × π × 15.5
C = 97.4 m
Total distance covered = 16 revolution × 97.4
Total distance covered = 1558.23 m
Total time taken = 4.5 × 60 = 270 s
Average angular speed = 1558.23 / 270
Angular speed = 5.77 rad/s
Therefore, your average angular speed is 5.77 rad/s
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26 miles and 385 yards to kilometers
To convert 26 miles and 385 yards to kilometers, we first need to convert miles and yards to the same unit.
1 mile = 1760 yards
26 miles = 26 x 1760 = 45600 yards
Then add the yards of the distance, so the total distance in yards is 45600+385 = 45985 yards
Now we can convert yards to kilometers.
1 yard = 0.9144 meters
45985 yards = 45985 x 0.9144 = 42.195 kilometers
So 26 miles and 385 yards is approximately 42.195 kilometers.
How did the Egyptians use chemistry?
Answer:
as far as I know they use chemistry to build pyramids block with reaction that why pyramids still exists
Answer: I hope this answer your question
Explanation:
The Egyptians were known in the ancient world as experts in many applied chemistry fields such as metallurgy, wine and beer making, glass making, paper manufacture, paint pigments, dyes, cosmetics, perfumes, and pharmaceuticals.Egyptians performed tasks that ranged from metallurgy to the production of dyes and pottery.They developed ways to measure time and distances , and applied their knowledge to monumental architecture.Used to build structures, manage the food supply and compute the flood levels of the Nile, math was vital to everyday life in Ancient Egypt. A remnant of their impressively sophisticated mathematical system, the Rhind Papyrus illustrates how Egyptians approached geometry, arithmetic and algebra.
A swimming fish has a momentum of 8 kg-m/s. It eats a stationary 2 kg fish and keeps
swimming. What is their new momentum?
a. Zero
b. 10 kg-m/s
c. 8 kg-m/s
d. 16 kg-m/s
Answer:
d. 16 kg-m/s
Explanation:
The new momentum of the swimming fish after eating the stationary fish can be calculated by adding the momentum of the initial swimming fish and the momentum of the stationary fish. Since momentum is a vector quantity, the direction of the momentum is the same as the direction of motion of the fish. If the fish continues to swim with the same velocity after eating the stationary fish, then the new momentum is the sum of the initial momentum of the swimming fish and the momentum of the stationary fish.
Initial momentum of swimming fish = 8 kg-m/s
Momentum of stationary fish = 2 kg * 0 m/s = 0 kg-m/s
New momentum = Initial momentum of swimming fish + Momentum of stationary fish = 8 kg-m/s + 0 kg-m/s = 8 kg-m/s + 2 kg-m/s = 10 kg-m/s.
So, the correct answer is (d) 16 kg-m/s.
Answer:
C
Explanation:
Using law of conservation of momentum of the system
Momentum before = momentum after
8 kg m/s = 8 kg m/s
The second fish has zero momentum, so after eating it the system still has momentum of 8 kg m/s
Please answer the question.
Answer:
Explanation:
bxvbrzfbd
Write down suitable function of p and q which could be plotted against each other so as to obtain straight line graph in the following cases: (a) Q= ap^n (b) Q^m=ap^n
Answer:
Explanation:
(a) Q=ap^n
Function of p and q:
p = q^(1/n)
(b) Q^m=ap^n
Function of p and q:
p = (q^(1/m))^(1/n)
A net force always result in a ________
Answer:
Explanation:
______?
Net forces always result in an acceleration. Newton's Second Law of Motion states that a net force (the sum of all forces acting on an object) will cause an object to accelerate in the same direction as the net force. The acceleration is proportional to the magnitude of the net force and inversely proportional to the mass of the object.
Answer:
A net force always result in a acceleration
The most powerful ice breaker in the world was built in the former Soviet Union. The ship is almost 150 m long, and its nuclear engine generates 56 MegaWatts (56 E^6 W) of power. How much work can this engine do in 1.0 hour? (1 hour = 3600 seconds)
The amount of work the engine can do in 1.0 hour, given that the engine generates 56 MegaWatts is 2016×10⁸ Joules
How do I determine the amount of work the engine can do?Work is defined as the product of force and distance moved in the direction of the force.
Work done (Wd) = force (F) × distance (d)
Power is defined as the rate at which work is done:
Power = Work / time
Using the power-work relationship formula above, we can detertmine the work the engine will do in 1.0 hour as follow:
Power = 56 MegaWatts = 56×10⁶ WattsTime = 1.0 hour = 3600 secondsWork =?Power = Work / time
Cross multiply
Work = Power × time
Work = 56×10⁶ × 3600
Work = 2016×10⁸ Joules
Therefore, we can conclude from the above calculation that the work the engine will do is 2016×10⁸ Joules
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how long will it take to heat 5 kg of water from 28 degrees Celsius to 88 degrees Celsius in an electric kettle taking 6 amperes from a 220 volt supply . Specific Heat capacity of water is 400 joules per kilogram kelvin. I need this ASAP! .I'll mark brainliest
Answer:
1.5 minutes
Explanation:
To find out how long it will take to heat 5 kg of water from 28 degrees Celsius to 88 degrees Celsius in an electric kettle, we can use the equation:
Q = mcΔT
Where Q is the heat energy added, m is the mass of the water, c is the specific heat capacity of water and ΔT is the change in temperature.
The heat energy added to the water can be calculated as:
Q = (5 kg) x (400 J/kg·K) x (88°C - 28°C) = (5 kg) x (400 J/kg·K) x (60°C) = 120000 J
The power of the electric kettle can be calculated using the formula:
P=VI
where P is the power, V is the voltage and I is the current,
P = (220 V) x (6 A)
= 1320 W
Now we can calculate the time it takes to heat the water by dividing the heat energy added by the power:
time = Q/P = 120000 J / 1320 W
= 90.909 seconds or 1.5 minutes
It will take 1.5 minutes to heat 5 kg of water from 28 degrees Celsius to 88 degrees Celsius in an electric kettle taking 6 amperes from a 220 volt supply.
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The purpose of the chiller is to
A. remove heat from the air.
B. cool conditioned air.
C. distribute the refrigerant.
D. cool warmed water.
The purpose of the chiller is to remove heat from the air and is therefore denoted as option A.
What is a Chiller?This is a type of device which is referred to as type of a cooling system that removes heat by circulating heat-absorbing a refrigerant through a series of mechanisms through which the heat is released.
The result of this process is that the heat in the air is removed as a result of the refrigerant being adequately circulated and then the environment becomes cooler and is therefore the reason why it was chosen as the correct choice.
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- The same mass of 5 different substances was used to heat the same mass of water in a simple
calorimeter. The results are shown below. Based on these results, which of these substances made
the worst fuel?
Answer:
Substance ΔH (kJ/g)
Coal -40.23
Hydrogen -242.82
Methanol -252.45
Octane -43.99
Propane -214.46
Explanation:
Methanol made the worst fuel because it has the lowest ΔH value of -252.45 kJ/g, which means that it releases the lowest amount of energy when used as a fuel. The other substances have higher ΔH values, so they produce more heat energy when burned.
To test the performance of its tires, a car
travels along a perfectly flat (no banking) circular track of radius 96.6 m. The car increases
its speed at uniform rate of
at ≡((d |v|)/dt) = 4.87 m/s^2
until the tires start to skid.
If the tires start to skid when the car reaches
a speed of 21.1 m/s, what is the coefficient of
static friction between the tires and the road?
The acceleration of gravity is 9.8 m/s^2
The coefficient of static friction between the tires and the road is 1.987.
What is Static friction?Radius of the track, r = 516 m, Tangential Acceleration = 3.89 m/s^2 and Speed,v = 32.8 m/s
The radial Acceleration is given by, Now the total acceleration is The frictional force on the car will be f = ma------------(1)
And the force due to gravity is W = mg--------------------(2)
Now the coefficient of static friction is, From (1) and (2), Substituting the values, we get friction is 1.987.
Therefore, The coefficient of static friction between the tires and the road is 1.987.
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A bullet of mass mb=11.9gr is being fired from a stationary gun of mass mg=2.1kg. If the velocity of the bullet is vb=235.1 m/s, what would be the recoil velocity of gun, vg, in m/s?
Answer:given that-
Bullet mass= 11.9gr
gun mass= 2.1
Velocity of bullets= 235.1m/s
A/q,
satisfied-
law of conservation of momentum
pf=pi
(Mass of gun+ mass of bullets)reserve velocity= mass of bullets ×velo of bullets
=>( 2100+11.9)vr=11.9×235.1
=>(2111.9 )vr=2797.69
=>vr=297.69/2111.9
vr=1.32m/
The truss shown in the figure carries a
load F= 20 kN at joint D. The truss is
designed with nine rods, six of which (the
inclined ones) have the same length d=2
m. Rods BC, EC, DE, and BD form a
square.
1. Find the support reactions at joints A
and F.
2. Using the method of joints or method of
sections to find the tensions in rods BD
and BC.
3. State whether each member is in
tension or compression.
The support reactions at joints A and F is 28.28 kN.
The method of joints or method of sections to find the tensions in rods BD and BC is 40 kN.
Each member is in tension or compression are (T_BC = 20 kN) and (T_BD = 40 kN).
What is compression?Compression is the process of reducing the size of a file, or data set, by encoding it using fewer bits than the original file. Compression techniques are used in many fields, including data storage and transmission, audio and video editing, and software development.
1. The support reactions at joints A and F can be found by using the equations of equilibrium:
R_A = F_x = 0 = -20 kN + R_F cos(45°)
R_F = F_y = 0 = -20 kN + R_A cos(45°)
Solving the equations, R_A = 28.28 kN and R_F = 28.28 kN.
2. Using the method of joints, the tensions in rods BC and BD can be found by taking moments around point D.
Moment about D: 0 = -F×d×sin(45°) + T_BC×d/2 - T_BD×d/2
Therefore, T_BC = 20 kN and T_BD = 40 kN.
3. Rod BC is in tension (T_BC = 20 kN) and rod BD is in compression (T_BD = 40 kN).
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Define the term " relative permittivity "
Answer:
Relative permittivity describes the ability to polarize a material subjected to an electrical field.
Explanation:
This polarization originates from a number of sources:
- electron cloud displaced relative to nucleus
- relative displacement of charged ions
- alignment of dipoles in electric field
- movement of charge carriers trapped by interfaces in heterogeneous systems
- movement of ionic charges
In simple terms, relative permittivity tells us how well a material can hold an electric charge. A material with a high relative permittivity can hold more electric charge than a material with a low relative permittivity.
You weigh 660 N.
What would you weigh if the Earth were
two times as massive as it is and its radius
were five times its present value?
Answer in units of N.
At a mass that is 2 times the current earth and a radius 5 times its value, your weight will be 52.8 N.
How do you find the new weight of the body?In general, we can assume a gravitational force of the following magnitude for any planet or mass:
[tex]F = \frac{Gm_{1} m_{2} }{r^{2} }[/tex]
where G = 6.67 x 10⁻¹¹m³/kgs², a universal gravitational constant.
m = masses of objects
r = radius of objects.
Given that W = 660 N
m₁ = 2Me, new mass of earth
r = 5re, new radius of earth
Then [tex]660 N = \frac{GM_{E} m}{r^{2}_{E} }[/tex]
Since [tex]F = \frac{GM m}{r^{2} }[/tex]
Substituting both new mass and radius;
[tex]F = \frac{G(2M_{E}) m}{(5r_{E})^{2}}[/tex]
[tex]F = \frac{2}{25} \frac{GM_{E} m}{r^{2}_{E}}[/tex]
Using the equation that weight is [tex]660 N = \frac{GM_{E} m}{r^{2}_{E} }[/tex]
[tex]F = \frac{2}{25}(660 N)[/tex] = 0.08 x 660 N
F = 52.8 N
Since the earth is 5 times its radius and twice its mass a weight of 650N will become 52.8 N.
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explain some of the technological challenges faced for deep space exploration. (ex. communication, flyby, slingshot effect, Hohmann Transfer orbits)
Answer:
Deep space exploration poses several technological challenges, including:
Explanation:
Maintaining contact with spacecraft is one of the fundamental difficulties in deep space exploration. Due to the time it takes for a signal to travel, communication delays increase as a spacecraft gets further away from Earth. The spacecraft's control and operation may be challenging as a result.
Flyby: Spacecraft frequently utilize the flyby approach to explore deep space. In this method, a spacecraft flies by a celestial body at a high speed while utilizing the planet's gravity to alter its course. To ensure that the spacecraft passes by at the appropriate altitude and speed, this strategy needs exact navigation and timing.
Slingshot effect: The slingshot effect, often referred to as gravity assist, is a method for accelerating a spacecraft by drawing on the gravitational pull of a planet or other celestial body. To make sure that the spacecraft does not collide with the celestial body or fly out into deep space, the trajectory must be carefully predicted.
Orbits used for Hohmann transfers: These orbits are effective for moving a spacecraft from one planet to another. To guarantee that the spacecraft is in the proper location at the appropriate moment to execute the transfer, this procedure, however, need exact calculations.
Power and propulsion: To function for long periods of time during deep space exploration, spacecraft need to have a dependable source of power and propulsion. Solar panels can provide electricity, but they are less effective in deep space, where the sun's light is faint. Alternative energy sources exist, however nuclear power has regulatory and safety issues. Propulsion systems must also be able to resist the severe conditions of deep space and function for extended periods of time.
Radiation protection: High-energy particles and radiation from deep space may kill humans and destroy electronic equipment. To mitigate against these risks, spacecraft must be developed, which can be challenging and expensive.
Cost: Deep space exploration is an expensive undertaking, requiring large investments in technology development, spacecraft design, and mission operations.
These are some of the technological challenges faced in deep space exploration, but it is important to note that many other challenges exist and new challenges will continue to arise as we explore more of the universe.
Daniel asks you to move the tables in his room. If there was no friction, you would have to push at 12 N to move the table. But there is no friction! Friction exerts a force of 3 N. You are only able to push at 7 N, so you get a friend to help. What force does your friend need to push to move the table?
Objects with masses of 141 kg and 494 kg are separated by 0.396 m. A 74.8 kg mass is placed midway between them.
1 ) Find the magnitude of the net gravitational force exerted by the two larger masses on the 74.8 kg mass.
The value of the universal gravitational constant is 6.672 × 10−11 N · m^2 /kg^2.
Answer in units of N.
2 ) Leaving the distance between the 141 kg and the 494 kg masses fixed, at what distance from the 494 kg mass (other than infinitely remote ones) does the 74.8 kg mass experience a net force of zero?
Answer in units of m.
( 1) The net gravitational force between the 74.8 kg mass is 8.09 x 10⁻⁵ N.
( 2) The distance from the from the 494 kg mass where the middle mass experiences net zero force is 0.258 m.
What is net gravitational force on the middle mass?The net gravitational force acting on the middle mass is calculated by applying Newton's law of universal gravitation as shown below.
F = ( GmM ) / ( R² )
where;
G is universal gravitation constantm is the mass of the middle massM is the mass of the first massR is the distance of separation between the two massesThe force between the first mass and the middle mass is calculated as;
F' = ( 6.672 x 10⁻¹¹ x 141 x 74.8 ) / ( 0.198² )
F' = 1.8 x 10⁻⁵ N
The force between the third mass and the middle mass is calculated as;
F'' = ( 6.672 x 10⁻¹¹ x 494 x 74.8 ) / ( 0.198² )
F'' = 6.29 x 10⁻⁵ N
The net gravitational force on the middle mass;
F (net) = 6.29 x 10⁻⁵ N + 1.8 x 10⁻⁵ N
F ( net ) = 8.09 x 10⁻⁵ N
Let the distance of zero net force from the 141 kg mass = d.
then the distance from the 494 kg mass = 0.396 m - d
F' = ( 6.672 x 10⁻¹¹ x 141 x 74.8 ) / ( d² )
F' = 0.704 x 10⁻⁶ / d²
F'' = ( 6.672 x 10⁻¹¹ x 494 x 74.8 ) / ( 0.396 - d )²
F'' = 2.47 x 10⁻⁶ / ( 0.396 - d )²
for zero net force, the two forces must be equal
0.704 x 10⁻⁶ / d² = 2.47 x 10⁻⁶ / ( 0.396 - d )²
0.704 (0.396 - d )² = 2.47d²
(0.396 - d )² = ( 2.47d² ) / ( 0.704 )
(0.396 - d )² = 3.51d²
0.396 - d = √ ( 3.51d² )
0.396 - d = 1.87d
1.87d + d = 0.396
d (1.87 + 1) = 0.396
d (2.87) = 0.396
d = 0.396 / 2.87
d = 0.138 m
The distance from the 494 kg mass = 0.396 - 0.138 m = 0.258 m
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A roller coaster is moving at 25 m/sec at the bottom of a hill. Three seconds later it reaches the top of the next hill, moving at 10m/sec. What is the acceleration (negative acceleration is slowing down) of the roller coaster?
Acceleration is the rate of change of velocity. It can be calculated using the formula:
a = (vf - vi) / t
Given:
vi = 25 m/s (initial velocity)
vf = 10 m/s (final velocity)
t = 3 s (time interval)
a = (vf - vi) / t = (10 m/s - 25 m/s) / 3 s = -15 m/s^2
The acceleration of the roller coaster is -15 m/s^2.
Negative acceleration indicates that the roller coaster is slowing down. This means that the roller coaster is losing speed as it reaches the top of the hill. The roller coaster is decelerating (negative acceleration) while it climbs the hill, so that it can move with a lower velocity at the top of the hill.
Reginald Esuke from Cameroon ran down a mountain slope in just 62.25 min. How much work was done if the power developed during Esuke's descent was 585.0 W?
The mountain slope is 585.0 W multiplied by 62.25 min, which is 36,378.75 joules.
What is slope?Slope is a measure of the steepness of a line. It is calculated by finding the ratio of the vertical change to the horizontal change between any two points on a line. Slope is represented by the letter m and is calculated by the equation m= (y2-y1)/(x2-x1). If the line is going up from left to right, the slope is positive. If the line is going down from left to right, the slope is negative. Slope is an important concept in mathematics, especially in calculus and linear algebra. It is used to find the rate of change between two points, as well as to determine the equation of a line.
The amount of work done is equal to the power developed multiplied by the time elapsed. Therefore, the work done by Reginald Esuke during his descent down the mountain slope is 585.0 W multiplied by 62.25 min, which is 36,378.75 joules.
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An object travels from (4,0) to (0,4) along path defined by x
2
+y
2
=16 under the applied force is
F
=(
x
2
+y
2
1
)i+(
x
2
+y
2
4
)j. Find the work done using the differential form of the work integral. Clearly show the work integral.
The work done on an object moving from position (x1, y1) to (x2, y2) under an applied force F is given by the work integral:
W = ∫ F ⋅ dr
where dr is the displacement vector from position (x1, y1) to (x2, y2).
For the given scenario, the applied force is F = (x^2 + y^2)i + (x^2 + y^2)^(1/2)j, and the displacement is from (4,0) to (0,4), which is given by dr = (-4, 4)i + (0, 4)j.
So, the work done is:
W = ∫ F ⋅ dr = ∫ ((x^2 + y^2)i + (x^2 + y^2)^(1/2)j) ⋅ ((-4)i + (4)j)
= ∫ -4x^2 - 4y^2 + 4(x^2 + y^2)^(1/2) dx
This work integral cannot be solved in closed form and will require numerical methods to evaluate the definite integral.
1. At what displacement the kinetic energy and potential energy of a particle executing SHM will be equal when the amplitude is 3cm?
The displacement at which the kinetic energy and potential energy of a particle executing SHM will be equal when the amplitude is 3cm is 1.5cm.
How does the amplitude of simple harmonic motion affect the ratio of kinetic to potential energy at a specific displacement?The amplitude of simple harmonic motion affects the ratio of kinetic to potential energy at a specific displacement in the following way: as the amplitude increases, the ratio of kinetic to potential energy decreases. This is because the amplitude represents the maximum displacement from the equilibrium position, and as the amplitude increases, the potential energy of the particle increases, while the kinetic energy remains constant. Therefore, at a specific displacement, a particle with a larger amplitude will have a greater proportion of its energy in the form of potential energy, while a particle with a smaller amplitude will have a greater proportion of its energy in the form of kinetic energy.
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How long will it take a pulse moving at 0, 25 m-s¹ to travel a distance of 20 m?
Answer:
T=80
Explanation:
soln
v=0.25ms
d=20m
t=?
therefore; velocity=distance/time taken
equating the valuables we have
0.25=20/t
making t the subject formula we have
t=20/0.25 => 80s
(PLEASE HELP) Place the following in order according to how fast light travels through them: Gas, Liquid, Solid, Vacuum.
Answer:
Light waves do not need a medium in which to travel but sound waves do. Explain that unlike sound, light waves travel fastest through a vacuum and air, and slower through other materials such as glass or water.
Explanation:
Light travels in a straight line as a wave. It does not require any medium or material to travel like sound waves which means it can travel in vacuum.The speed of the light from the special theory of relativity is a constant value of 38x10^8m/second
Does a series connection between capacitors always result in equal amount of charge being stored in each capacitor
Answer:
Yes - If a charge of +Q is removed from one side of a battery, a charge of -Q must be removed from the other side of the battery, the charges on the intervening capacitors are likewise equal.
Momentum Principle please help
The momentum of the ball is
(-0.18, -0.40, 0.20)m
What is momentum?Generally, The momentum principle, also known as Newton's second law of motion, states that the rate of change of momentum of an object is equal to the force applied to it. Mathematically, this can be expressed as:
F = d(mv)/dt
where
F is the force applied, m is the mass of the object, v is the velocity of the object, and t is time.To determine the position of the ball 0.1 seconds later, we need to know the force acting on the ball due to the elastic band. This force is given by Hooke's Law, which states that the force acting on an object due to a spring is equal to the spring constant (k) multiplied by the displacement of the spring from its relaxed position. In this case, the spring constant is 0.9 N/m, and the displacement is the difference in length between the relaxed length (0.3 m) and the current length of the elastic band.
We know that the ball is at location (-0.2, -0.61, 0)m relative to the point where the elastic band is attached to the paddle. We can find the length of the elastic band by using the distance formula:
√((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2 ) = √((-0.2 - 0)^2 + (-0.61 - 0)^2 + (0 - 0)^2 )
= √(0.04 + 0.3721 + 0)
= √0.4121
= 0.63874m
The displacement of the spring is the relaxed length (0.3 m) minus the current length of the elastic band (0.63874 m), which is -0.33874 m. The force acting on the ball due to the elastic band is
-0.9 * -0.33874 = 0.30486 N.
We can use the force to find the acceleration of the ball using Newton's second law,
F = ma.
Since the mass of the ball is 0.015 kg, the acceleration of the ball is
0.30486 N / 0.015 kg = 20.324 m/s^2
We can use this acceleration to find the final velocity of the ball using the equation vf = vi + at.
Since the initial velocity of the ball is
(-0.02, -0.01, -0.02) kg-m/s, the final velocity of the ball is
(-0.02, -0.01, -0.02) + (20.324, 20.324, 20.324) * 0.1 s = (-0.02, -0.01, -0.02) + (2.0324, 2.0324, 2.0324)
= (2.0124, 2.0224, 2.0124) m/s
The final position of the ball can be found using the equation
xf = xi + vt.
The initial position of the ball is (-0.2, -0.61, 0)m and the final velocity is (2.0124, 2.0224, 2.0124) m/s, so the final position of the ball after 0.1 s is
(-0.2, -0.61, 0) + (2.0124, 2.0224, 2.0124) * 0.1 s
= (-0.2, -0.61, 0) + (0.20124, 0.20224, 0.20124)
= (-0.18, -0.40, 0.20)m
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Several vectors in the x-y plane are shown in the figure with their tails at the origin of the coordinate system and with a label at their heads. Two of these vectors are given in terms of the unit-vectors i and j as P = (2.80i + 2.30j) and Q = (-3.90i + 1.20j), where the numbers are measured in meters. Let M = (P+Q). Calculate the magnitude of the vector M.
Several vectors in the x-y plane are shown in the figure with their tails at the origin of the coordinate system and with a label at their heads.The value of M = (P+Q) is
3.65 meters
What is magnitude?Generally, To calculate the magnitude of the vector M = P + Q, we need to use the Pythagorean theorem.
M = P + Q
M= (2.80i + 2.30j) + (-3.90i + 1.20j)
M= (-1.10i + 3.50j)
The magnitude of the vector M is the square root of the sum of the squares of the x and y components of the vector.
|M| = √((-1.10)^2 + (3.50)^2)
= √(1.21 + 12.25)
= √13.46
≈ 3.65 meters
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A highway curves to the left with radius of
curvature of 36 m and is banked at 25 ◦
so
that cars can take this curve at higher speeds.
Consider a car of mass 1091 kg whose tires
have a static friction coefficient 0.87 against
the pavement.
How fast can the car take this curve without
skidding to the outside of the curve? The
acceleration of gravity is 9.8 m/s^2.
Answer in units of m/s.
The car can take this curve at a speed of 18.8 m/s without skidding to the outside of the curve
How do we calculate the speed to which the car can move?The maximum speed at which a car can take a curved road without skidding outward is given by the formula:
v = √(g * r * (cos(theta) + (mu * sin(theta))/mu_s))
where:
v = velocity of the car
g = acceleration due to gravity (9.8 m/s^2)
r = radius of curvature of the road (36 m)
theta = angle of banking of the road (25 degrees)
mu = coefficient of friction between the tires and the road (0.87)
mu_s = coefficient of static friction between the tires and the road (0.87)
So the maximum speed at which the car can take this curve without skidding is:
v = √(9.8 * 36 * (cos(25) + (0.87 * sin(25))/0.87))
v = √(9.8 * 36 * (0.9063 + 0.4696))
v = √(9.8 * 36 * 1.376)
v = √(352.48)
v = 18.8 m/s
Therefore, the car can take this curve at a speed of 18.8 m/s without skidding to the outside of the curve.
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A 1,000 kg hot air balloon is drifting along at 3 m/s at a height of 50m above the ground.
How much kinetic energy does the balloon have? ___
How much potential energy does the balloon have? ____
How much total mechanical energy does the balloon have? ___
The Kinetic energy of the hot air balloon is 4500 Joules, the potential energy is 4.9 × 10⁵ Joules, and the total mechanical energy is 4.95 × 10⁵ Joules.
What is the Kinetic energy?The Kinetic energy is the amount of energy which is present in the body of an object which is under motion. The kinetic energy is a vector quantity because it has both the magnitude and direction. The SI unit of KE is Joule. The KE of an object can be calculated by the formula:
KE = 1/2 mv²
KE = 1/2 × 1000 × (3)²
KE = 500 × 9
KE = 4500 Joules
PE = m × g × h
PE = 1000kg × 9.8 × 50
PE = 490,000 Joules
Total Mechanical energy = PE + KE
Total Mechanical energy = 4500 + 490000
Total Mechanical energy = 494500 Joules
Total Mechanical energy = 4.95 × 10⁵ Joules
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A hiker walks 27.0 km from her base camp at 35° south of east. The next day, she walks 41.0 km in a direction 65° north of east and discovers a forest ranger's tower. Find the magnitude and direction of her resultant displacement between the base camp and the tower.
The magnitude and direction of the hiker's resultant displacement is 42.7 km, 64.6° north of east.
How to find the magnitude and direction?To find the magnitude and direction of the hiker's resultant displacement, we can use vector addition.
First, we need to convert the given magnitudes and directions into x and y components. We can use trigonometry to do this:
x component of the first displacement = 27.0 km * cos(35°) = 21.5 km
y component of the first displacement = 27.0 km * sin(35°) = 15.5 km
x component of the second displacement = 41.0 km * cos(65°) = 17.6 km
y component of the second displacement = 41.0 km * sin(65°) = 30.6 km
Now we can add the x and y components of each displacement to find the x and y components of the resultant displacement:
x component of the resultant displacement = 21.5 km + 17.6 km = 39.1 km
y component of the resultant displacement = 15.5 km + 30.6 km = 46.1 km
To find the magnitude of the resultant displacement, we can use the Pythagorean theorem:
magnitude of the resultant displacement = sqrt(39.1 km^2 + 46.1 km^2) = sqrt(1820.81 km^2) = 42.7 km
Finally, we can use the arctangent function to find the direction of the displacement:
direction = arctan(46.1 km / 39.1 km) = 64.6° north of east.
So the magnitude and direction of the hiker's resultant displacement is 42.7 km, 64.6° north of east.
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