Answer:
[tex]velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex]
Max speed = [tex]\frac{15\, \pi}{4} \,\, \frac{m}{s}[/tex]
Max acceleration = [tex]\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}[/tex]
Explanation:
Given the description of period and amplitude, the SHM could be described by:
[tex]f(x)=5\,sin(\frac{\pi}{4}x)[/tex]
and its angular velocity can be calculated doing the derivative:
[tex]f(x)=5\, \,sin(\frac{\pi}{4}x)\\f'(x)=5\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex]
And therefore, the tangential velocity is calculated by multiplying this expression times the radius of the movement (3 m):
[tex]velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex] and is given in m/s.
Then the maximum speed is obtained when the cosine function becomes "1", and that gives:
Max speed = [tex]\frac{15\, \pi}{4} \,\, \frac{m}{s}[/tex]
The acceleration is found from the derivative of the velocity expression, and therefore given by:
[tex]acceleraton(x)=-15\,\frac{\pi^2}{16}\,sin(\frac{\pi}{4}x)[/tex]
and the maximum of the function will be obtained when the sine expression becomes "-1", which will render:
Max acceleration = [tex]\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}[/tex]
A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10 m/s due north relative to the water.(a) What is the velocity of the boat relative to the shore?(b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?
Answer:
a
[tex]u = 10.11 \ m/s[/tex]
b
[tex]x = 44.996 \ m[/tex]
Explanation:
From the question we are told that
The velocity of the river due east is [tex]v = 1.150i \ m /s[/tex]
The velocity of the boat due north is [tex]v_1 = 10j \ m/ s[/tex]
The width of the river is [tex]d = 300 \ m[/tex]
Generally the velocity of the boat relative to the shore
[tex]u = \sqrt{v^2 + v_1^2}[/tex]
=> [tex]u = \sqrt{1.50 ^2 + 10^2}[/tex]
=> [tex]u = 10.11 \ m/s[/tex]
Generally direction of the boat relative to the shore is mathematically represented as
[tex]tan \theta = \frac{v}{v_1}[/tex]
=> [tex]\theta = tan^{-1}[ \frac{v}{v_1}][/tex]
=> [tex]\theta = tan^{-1}[ \frac{1.5}{10}][/tex]
=> [tex]\theta = 8.53^o[/tex]
Generally the distance covered by the boat in the direction of flow of the river before reaching the north shore is mathematically represented as
[tex]x = d* tan(\theta )[/tex]
=> [tex]x = 300 * tan(8.53)[/tex]
=> [tex]x = 44.996 \ m[/tex]
(a) The velocity of the boat relative to the shore is 10.11 m/s.
(b) The distance traveled by the boat when it reaches the north shore is 303.3 m.
The given parameters;
initial velocity of the river, = 1.5 m/s due eastvelocity of the boat, = 10 m/s due north(a) The velocity of the boat relative to the shore is calculated by applying Pythagoras theorem as shown below;
[tex]v = \sqrt{1.5^2 + 10^2} \\\\v = 10 .11 \ m/s[/tex]
(b) Let the time taken for the boat to reach the north shore = t
[tex]distance = speed \times time \\\\c^2 = a^2 + b^2\\\\[/tex]
the width of the river is the height of the right-trianglethe displacement of the river after time "t" is the base of the right-trianglethe displacement of the boat after time "t" is the hypotenuse side[tex](10.11t)^2 = (300)^2 + (1.5t)^2\\\\102.21t^2 = 90,000 + 2.25t^2\\\\99.96t^2 = 90,000\\\\t^2 = \frac{90,000}{99.96} \\\\t^2 = 900\\\\t = \sqrt{900} \\\\t = 30 \ s[/tex]
The distance traveled by the boat when it reaches the north shore;
[tex]d = 10.11t\\\\d = 10.11 \times 30\\\\d = 303.3 \ m[/tex]
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Newton's 2nd Law describes the relationship between force, mass, and acceleration of an object with the formula F=ma. Which scenario below will result in the greatest accleration? (AKS 8b / DOK 1)
A. A 20 kg rock thrown with a 100 N force.
B. A 10,000 kg rocket launched with 100,000 N of force.
C. A 2,000 kg car accelerated with a 1000 N force from the engine.
D. A 50 kg student pushed in a chair with a force of 1000 N.
Answer:D
Explanation:If you want to find the acceleration do Force/mass.
The greatest magnitude of acceleration is of 20 m/s², by the student of 50 kg pushing the chair with 1000 N of force. Hence, option (D) is correct.
As per the Newton's second law, " The applied force on an object is equal to the product of mass of object and acceleration cause by the applied force. Then, the mathematical expression is,
F = ma
Here, F is the applied force, m is the mass and a is acceleration.
(A)
For 20 kg mass and 100 N force, the acceleration is,
F = ma
100 = (20)a
a = 5 m/s²
(B)
For 10,000 kg mass of rocket and 100,000 N force, the acceleration is,
F = ma
100 ,000= (10,000)a
a = 10 m/s²
(C) For a 2,000 kg mass of car and force of 1000 N, the acceleration is,
F = ma
1000 = (2000)a
a = 0.5 m/s²
(D) For a mass of 50 kg student and applied force of 1000 N, the acceleration is,
F = ma
1000 = (50)a
a =20 m/s².
Thus, we can conclude that the greatest magnitude of acceleration is of 20 m/s², by the student of 50 kg pushing the chair with 1000 N of force. Hence, option (D) is correct.
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How long would it take a boat that started at rest to get to a velocity of 56 m/s if it was accelerating at 17 m/s/s?
Answer:
3.29 s
Explanation:
Using v = u + at where u = initial velocity of boat = 0 m/s since it starts at rest, v = final velocity of boat = 56 m/s, a = acceleration of boat = 17 m/s² and t = time taken to accelerate to 56 m/s.
So, v -= u + at
t = (v - u)/a
substituting the values of the variables, we have
t = (56 m/s - 0 m/s)/17 m/s²
= 56 m/s ÷ 17 m/s²
= 3.29 s
It will take the boat 3.29 s to accelerate to 56 m/s at an acceleration of 17 m/s²
If earth squeezed to the size of moon.Calculate the weight of 100kg mass in the squeezed earth.
Answer:
833.9kg that's the answer
if an atom has two protons and three electrons than the atom is
Answer:
negative 1 charge
Explanation:
one electron is extra so there will be -1 chargw
If an atom has two protons and three electrons than the atom is negatively charged.
What is an atom?An atom is a matter particle that defines a chemical element uniquely. An atom is made up of a central nucleus and one or more negatively charged electrons.
The nucleus is positively charged and contains one or more protons and neutrons, which are relatively heavy particles.
It is made up of protons, which have a positive charge, and neutrons, which do not have any charge. Protons, neutrons, and the electrons that surround them are long-lived particles found in all natural atoms.
The modern atomic hypothesis was founded by John Dalton, a great chemist. His atom, on the other hand, was like a solid billiard ball.
An atom is negatively charged if it has two protons and three electrons.
Thus, the given atom bears negative charge.
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A diver 50 m deep in 10∘C fresh water exhales a 1.0-cm-diameter bubble. What is the bubble's diameter just as it reaches the surface of the lake, where the water temperature is 20∘C?
Answer:
18.2mm
Explanation:
D = 50m
T1 = 10+273 = 283K
T2 = 20+273 = 293K
R1 = 5x10^-3
Absolute pressure at 50m
P1 = pA + pwateer x g x d
= 101000+ 1000x9.81x50
= 591500pa
New volume of bubble
= P1v1/T1 = p2v2/T2
= 125x10^-9 x 591500x293/101000*283
= 757.9x10^-9m³
R2 = 9.2x10^-3
D2 = 18.2mm
Or 1.82cm
Hypoventilation dramatically increases carbonic acid concentration and involves________?
extremely fast breathing
extremely slow breathing
irregular breathing
intermittent breathing
extremely deep breathing
Which has more momentum, a 2000 lb car moving at 100 km/hr or a 4000 lb truck moving at 50 km/hr ?
Answer:
The truck and car have the same momentum.
Explanation:
[tex]m_1[/tex] = Mass of car = [tex]2000\ \text{lb}=2000\times0.45359237\ \text{kg}[/tex]
[tex]v_1[/tex] = Velocity of car = [tex]\dfrac{100}{3.6}\ \text{m/s}[/tex]
[tex]m_2[/tex] = Mass of truck = [tex]4000\times0.45359237\ \text{kg}[/tex]
[tex]v_2[/tex] = Velocity of truck = [tex]\dfrac{50}{3.6}\ \text{m/s}[/tex]
Momentum of car
[tex]p_1=m_1v_1\\\Rightarrow p_1=2000\times0.45359237\times \dfrac{100}{3.6}\\\Rightarrow p_1=25199.58\ \text{kg m/s}[/tex]
Momentum of the truck
[tex]p_2=m_2v_2\\\Rightarrow p_2=4000\times0.45359237\times \dfrac{50}{3.6}\\\Rightarrow p_2=25199.58\ \text{kg m/s}[/tex]
Both the truck and car have the same momentum of [tex]25199.58\ \text{kg m/s}[/tex].
If the radius of a sphere increases by a factor of 2.50, by what factor does the volume of the sphere change?
Answer:
.................
Explanation:
....
...............
A nearsighted person has a far point of 40cm. What power spectacle lens is needed if the lens is 2cm from the eye
Answer:
The value is [tex]p = - 2.63 \ Diopters[/tex]
Explanation:
From the question we are told that
The value of the far point is [tex]a = 40 \ cm = 0.4 \ m[/tex]
The distance of the lens to the eye is [tex]b = 2 \ cm = 0.02[/tex]
Generally
[tex]1 Diopter = > 1 m^{-1}[/tex]
Generally the power spectacle lens needed is mathematically represented as
[tex]p = \frac{1}{d_o } + \frac{1}{d_i}[/tex]
Here [tex]d_o[/tex] is the object distance which for a near sighted person is [tex]d_o = \infty[/tex]
And [tex]d_i[/tex] is the image distance which is evaluated as
[tex]d_i = b - a[/tex]
=> [tex]d_i = 0.02 - 0.4[/tex]
=> [tex]d_i = -0.38 \ m[/tex]
So
[tex]p = \frac{1}{\infty } + \frac{1}{-0.38}[/tex]
=> [tex]p = 0 - 2.63[/tex]
=> [tex]p = - 2.63 \ Diopters[/tex]
Please help me on this with a full explanation
Answer:
a = 5 [m/s²]
Explanation:
We must perform a sum of forces on both axes (vertical axis and horizontal axis).
We see that the forces on the vertical axis are the same but in the opposite direction. In this way, there is no movement on the vertical axis y. and we can find the mass of the body.
∑Fy = 0
Fnorm - Fgrav = 0
We know that the force of gravity is equal to the product of mass by gravitational acceleration.
[tex]F_{grav}=m*g[/tex]
where:
m = mass [kg]
g = gravity acceleration = 10 [m/s²]
[tex]100=m*10\\m=100/10\\m=10[kg][/tex]
Since there is only one force on the horizontal axis, this force generates accelerated motion. This force is equal to the product of mass by acceleration, as stipulated by Newton's second law.
∑F = m*a
where:
F = force = 50 [N]
a = acceleration of the body [m/s²]
[tex]F=m*a\\50*10*a\\a=5[m/s^{2} ][/tex]
A 30 kg table is pushed forward with a force of 12 N. Friction pushes back with a
force of 5 N. What is the net force?!!
Answer:
a = 0.23 [m/s²]
Explanation:
To solve this problem we must use Newton's second law, which tells us that the sum of forces on a body is equal to the product of mass by acceleration.
∑F = m*a
where:
F = forces applied [N]
m = mass = 30 [kg]
a = acceleration [m/s²]
Now we can use Newton's second law, with forces pointing to the right as positives and negative forces pointing towards the left.
[tex]12 - 5 = 30*a\\7 = 30*a\\a = 0.23 [m/s^{2} ][/tex]
1. If an object does not change its position, then we say that it is at _________?
2. According to the video, can an object ALWAYS seem at rest to everyone?
3. What else did the person need in the video to find their friend's house BESIDES a REFERENCE POINT?
4. So according to the video, in order to find an object or place, you need what 3 things?
5. Using the number system to determine motion, what was the starting position of the car in the problem?
6. What was the final position of the car?
7. How far in total did the car actually travel?
Answer:
ᏌᎳᏆᎿᏌᎭ ᎭᏆᎳ ᎷᎭᏌ Ꭽ
Explanation:
Answer:
rest
Explanation:
if an object is not in it's position, then we say it is at rest.
Alex, parked by the side of an east-west road, is watching car P, which is moving in a westerly direction. Barbara, driving east at a speed 52 km/h, watches the same car. Take the easterly direction as positive. If Alex measures a speed of 78 km/h for car P, what velocity will Barbara measure?
Answer:
[tex]v_{PB} = 130\ km/h[/tex]
Explanation:
Since, Alex is at rest. Therefore, the speed measured by him will be the absolute speed of car P. Therefore, taking easterly direction as positive:
[tex]Absolute\ Velocity\ of\ Car\ P = v_{P} = -78\ km/h[/tex]
And the absolute velocity of Barbara's Car is given as:[tex]Absolute\ Velocity\ of\ Barbara's\ Car = v_{B} = 52\ km/h[/tex]
Now, for the velocity of Car p with respect to the velocity of Barbara's Car can be given s follows:
[tex]Velocity\ of\ Car\ P\ measured\ by\ Barbara = v_{PB} = v_{B}-v_{P}\\\\v_{PB} = 52\ km/h-(-78\ km/h)[/tex]
[tex]v_{PB} = 130\ km/h[/tex]
When a falling meteoroid is at a distance above the Earth's surface of 3.40 times the Earth's radius, what is its acceleration due to the Earth's gravitation
Answer:
g = 0.85 m[tex]s^{-2}[/tex]
Explanation:
g = [tex]\frac{GM}{h^{2} }[/tex]
were; g is the acceleration due to Earth's gravity, G is Newton's gravitation constant (6.674 x [tex]10^{-11}[/tex] N[tex]m^{2}[/tex][tex]kg^{-2}[/tex]), M is the mass of the earth (5.972 x [tex]10^{24}[/tex] kg), and h is the distance of meteoroid to the earth.
h = 3.40 x R
= 3.40 x 6371 km
h = 21661.4 km
= 21661400 m
Thus,
g = [tex]\frac{6.674*10^{-11}*5.972*10^{24} }{(21661400)^{2} }[/tex]
= [tex]\frac{3.9857 *10^{14} }{4.6922*10^{14} }[/tex]
= 0.84944
g = 0.85 m[tex]s^{-2}[/tex]
The acceleration due to the Earth's gravitation is 0.85 m[tex]s^{-2}[/tex].
In a house, 3 bulbs of 60 watt each are lighted for 3 hours daily, 4 fans of 100 watt each are used for 8 hours daily and an electric heater of 2 kwh used for half an hour daily. Calculate the total energy consumed in a month of 31 days and its cost at the rate of Rs 4/kwh.
Answer:
Total Energy consumed = 146.94 kwh
Total cost = rs 587.76
Explanation:
Given:
3 bulbs each 60 watt [for 3 hours daily]
4 fans each 100 watt [for 8 hours daily
1 electric heater of 2 kWh (2,000 watt) [for half hour daily ]
Rate = rs 4/Kwh
Find:
Total Energy consumed
Total cost
Computation:
Energy used = Power × time
3 bulbs each 60 watt [for 3 hours daily] = 3 x 60 x 3 x 31 = 16,740 watt = 16.74 kw
4 fans each 100 watt [for 8 hours daily = 4 x 100 x 8 x 31 = 99,200 watt = 99.2 kw
1 electric heater of 2 kWh [for half hour daily ] = 1 x 2000 x (1/2) x 31 = 31,000 watt = 31 kw
Total Energy consumed = 16.74 + 99.2 + 31
Total Energy consumed = 146.94 kwh
Total cost = 146.94 x 4
Total cost = rs 587.76
If you wanted to find a sample of fermium, which has an atomic number of 100, where would you look?
A. Deep within the earth
B. In the earths atmosphere
C. In outer space
D. In Science Lab
Answer:
B
Explanation:
Fermium is a synthetic element with the symbol Fm and atomic number 100. It is an actinide and the heaviest element that can be formed by neutron bombardment of lighter elements, and hence the last element that can be prepared in macroscopic quantities, although pure fermium metal has not yet been prepared.[3] A total of 19 isotopes are known, with 257Fm being the longest-lived with a half-life of 100.5 days.
It was discovered in the debris of the first hydrogen bomb explosion in 1952, and named after Enrico Fermi, one of the pioneers of nuclear physics. Its chemistry is typical for the late actinides, with a preponderance of the +3 oxidation state but also an accessible +2 oxidation state. Owing to the small amounts of produced fermium and all of its isotopes having relatively short half-lives, there are currently no uses for it outside basic scientific research.
What is the relationship between elastic collision and 1:1 ratio?
An elastic collision is an come across between two bodies wherein the overall kinetic electricity of the two bodies stays the same.
In a super, perfectly elastic collision, there's no internet conversion of kinetic strength into other kinds inclusive of heat, noise, or capacity strength. An elastic collision is a collision wherein there is no internet loss in kinetic strength within the gadget due to the collision. each momentum and kinetic energy are conserved portions in elastic collisions.
An elastic collision is a collision wherein there is no internet loss in kinetic electricity in the gadget because of the collision. In the elastic collision, in which the kinetic energy is conserved, the kinetic electricity in an inelastic collision isn't always conserved. In an inelastic collision, the kinetic energy among the colliding bodies is exceptional at the start and the quit of the collision.
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Why is the term negative acceleration used instead of deceleration
Answer:
See Explanation
Explanation:
Whenever a force is applied in an object in the opposite direction of its motion. It tends to slow down the speed of the object. Therefore, this force is called the decelerating force and the acceleration produced by it is called deceleration.
The deceleration produced in this case by this decelerating force has a direction opposite to the direction of motion or velocity of the object. Therefore, this deceleration is defined with a negative sign along with its magnitude.
Due to this opposite direction, term negative acceleration is also used instead of deceleration.
What is the mass of a pet cat that weighs 75N?
Answer:
7.64787 kilograms
Explanation:
75 Newton = 7.64787 Kilograms
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pls mark brainliest :D
Answer:
Explanation:
sdfgbaewtfhsertfxzdfhaethsdhdsgfhds
What is the distance traveled
The projectile will travel 6053.13 m in the horizontal direction
Data obtained from the questionThe following data were obtained from the question:
Initial velocity (u) = 342 m/sAngle of projection (θ) = 66.3 degreesAcceleration due to gravity (g) = 9.8 m/s²Air resistance = 31.1%Range (R) =?How to determine the range of the projectileThe range the projectile will attain can be obtained as follow:
R = u²Sine(2θ) / g
R = 342² × Sine (2×66.3) / 9.8
R = 8785.39 m
Air resistance is 31.1%. Thus, we have
R = 8785.39 - (8785.39 × 31.1%)
R = 8785.39 - 2732.26
R = 6053.13 m
Thus, the projectile will travel 6053.13 m in the horizontal direction
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A person walks 5 meters north, which is vector 1. Then he walks 4 meters east, which is vector 2. The displacement vector is vector 3. Draw the vectors and calculate displacement and the angle between vectors 1 and 3
Explanation:
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The energy of microwaves is less than the energy of ultraviolet light. Which comparison of the energies of
electromagnetic waves is correct?
O Gamma rays have higher energy than microwaves because gamma rays have shorter wavelengths.
O Gamma rays have higher energy than microwaves because gamma rays have lower frequencies.
O Infrared light has lower energy than X-rays because infrared light has shorter wavelengths.
O Infrared light has lower energy than X-rays because infrared light has higher frequencies.
Answer:
A. Gamma rays have higher energy than microwaves because gamma rays have shorter wavelengths.
Explanation:
Electromagnetic waves are waves produced by the interaction between both magnetic and electric fields. These waves have some properties that make them to be arranged in a definite form producing an electromagnetic spectrum.
The spectrum has a general property of which as the wavelength of the waves increases, the frequency decreases. And vice versa.
Thus, the energy of the waves increases as the frequency increases.
Gamma rays have higher frequency, but shorter wavelength. While microwaves has lower frequency, but higher wavelength.
Answer:
Yes, the answer is A
Explanation:
define electric potential at a point and find expression for it.
Answer:
Recall that the electric potential is defined as the potential energy per unit charge, i.e. V=PEq V = PE q . ... The equation for the electric potential due to a point charge is V=kQr V = kQ r , where k is a constant equal to 9.0×109 N⋅m2/C2.
Explanation:
A satellite of 2,140 kg travels around the earth, of 5.97 - 1024
kg. How long will it take the satellite to complete one full orbit if
the distance between them is 9,325 km?
Answer:
8,961
Explanation:
a pendulum oscillates 25 times in 5 seconds calculate itrs time period and frequency
Answer:
I. Time period = 0.2 seconds.
II. Frequency = 5 Hertz.
Explanation:
Given the following data;
Time, t = 5 seconds.
Number of oscillation, n = 25 times
I. To find the time period;
[tex] Time \; period = \frac {time}{number \; of \; oscillations}[/tex]
Substituting into the equation, we have;
[tex] Time \; period = \frac {5}{25}[/tex]
Time period = 0.2 seconds.
II. To find frequency;
[tex] Frequency = \frac {1}{Time \; period}[/tex]
Substituting into the equation, we have;
[tex] Frequency = \frac {1}{0.2}[/tex]
Frequency = 5 Hertz.
Therefore, the time period and frequency of the pendulum is 0.2 seconds and 5 Hertz respectively.
Given the data in the question;
Number of oscillation in time t; [tex]n = 25[/tex]
Time taken for the oscillation; [tex]t = 5s[/tex]
Time period
Using the expression for Time period:
[tex]Time \ period = \frac{t}{Number\ of\ oscillation}[/tex]
We substitute our given value into the equation
[tex]Time \ period = \frac{5s}{25}\\\\Time \ period = 0.2s[/tex]
Hence, the time period is 0.2 seconds
Also, using the formula for frequency:
[tex]f = \frac{1}{T}[/tex]
Where f is frequency and T is time period.
We substitute our values into the equation
[tex]f = \frac{1}{0.2s} \\\\f = 5s^{-1}\\\\f = 5Hz[/tex]
Therefore, the frequency of the pendulum is 5 Hertz.
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the question is in a picture
Answer:
same for all objects
Explanation:
earth pulls every object by same force of gravity
What does human ethics mean?
Get a little long
Thanks
Explanation:
Ethics, also called moral philosophy, the discipline concerned with what is morally good and bad and morally right and wrong. The term is also applied to any system or theory of moral values or principles. Its subject consists of the fundamental issues of practical decision making, and its major concerns include the nature of ultimate value and the standards by which human actions can be judged right or wrong.
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According to Newton's second law, if you increase the mass but the force is the same, what happens to the acceleration?
Audio Recording 50 KB
acceleration decreases
Оа
Ob
Ос
acceleration increases
acceleration remains the same
Simple Answer. Mass cannot change.
Force=Acceleration
Electric circuits provide energy for light bulbs. Which of these prevents the flow of electrons?
O a circuit that is closed
O a series circuit
O a circuit that is open
O a parallel circuit
A circuit that is closed prevents the flow of electrons. So, the correct option is A.
What is an Electric circuit?An electrical circuit is defined as an interconnection of electrical components or a model of such interconnection, consisting of electrical elements. An electrical circuit is described as a network consisting of a closed loop, which provides a return path for current.
A closed circuit is required to carry current. When there is a break anywhere in the path, the circuit will open and no current will flow, and the metal atoms in the wire will quickly become cool and electrically neutral.
Thus, a circuit that is closed prevents the flow of electrons. So, the correct option is A.
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