Answer:
ffffffffffffffffffffffffffffffffffffffff
Explanation:
The jumper will take 0.419 seconds to reach the highest point.
What is Projectile Motion?A projectile can be described as an object that is thrown obliquely near the surface, it moves along a curved path with constant acceleration directed toward the center of the earth.
In a Projectile Motion, along the x-axis, there is uniform velocity, responsible for the horizontal motion, and along the y-axis, there is uniform acceleration, responsible for the vertical motion of the particle.
The time required to attain the maximum height of the jumper will be given by:
[tex]t =\frac{usin\theta}{g}[/tex]
Given, the velocity of the jumper, u = 12 m/s
The angle of the jumper with the horizontal, θ = 20°
The time taken by the jumper to achieve maximum height:
[tex]t = \frac{12\times sin 20}{9.8}[/tex]
t = 0.419 sec
Therefore, the jumper will achieve maximum height in 0.419 seconds.
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A rod of length Lo moves iwth a speed v along the horizontal direction. The rod makes an angle of (θ)0 with respect to the x' axis.
Required:
a. Show that the length of the rod as measured by a stationary observer is L=L0[1-v^2/c^2 cos^2(θ)0].
b. Show that the angle the rod makes iwth the x-axis is given by the expression tan(theta)=tan(θ)0/(1-v^2/c^2)^.5
Answer:
From the question we are told that
The length of the rod is [tex]L_o[/tex]
The speed is v
The angle made by the rod is [tex]\theta[/tex]
Generally the x-component of the rod's length is
[tex]L_x = L_o cos (\theta )[/tex]
Generally the length of the rod along the x-axis as seen by the observer, is mathematically defined by the theory of relativity as
[tex]L_xo = L_x \sqrt{1 - \frac{v^2}{c^2} }[/tex]
=> [tex]L_xo = [L_o cos (\theta )] \sqrt{1 - \frac{v^2}{c^2} }[/tex]
Generally the y-component of the rods length is mathematically represented as
[tex]L_y = L_o sin (\theta)[/tex]
Generally the length of the rod along the y-axis as seen by the observer, is also equivalent to the actual length of the rod along the y-axis i.e [tex]L_y [/tex]
Generally the resultant length of the rod as seen by the observer is mathematically represented as
[tex]L_r = \sqrt{ L_{xo} ^2 + L_y^2}[/tex]
=> [tex]L_r = \sqrt{[ (L_o cos(\theta) [\sqrt{1 - \frac{v^2}{c^2} }\ \ ]^2+ L_o sin(\theta )^2)}[/tex]
=> [tex]L_r= \sqrt{ (L_o cos(\theta)^2 * [ \sqrt{1 - \frac{v^2}{c^2} } ]^2 + (L_o sin(\theta))^2}[/tex]
=> [tex]L_r = \sqrt{(L_o cos(\theta) ^2 [1 - \frac{v^2}{c^2} ] +(L_o sin(\theta))^2}[/tex]
=> [tex]L_r = \sqrt{L_o^2 * cos^2(\theta) [1 - \frac{v^2 }{c^2} ]+ L_o^2 * sin(\theta)^2}[/tex]
=> [tex]L_r = \sqrt{ [cos^2\theta +sin^2\theta ]- \frac{v^2 }{c^2}cos^2 \theta }[/tex]
=> [tex]L_o \sqrt{1 - \frac{v^2}{c^2 } cos^2(\theta ) }[/tex]
Hence the length of the rod as measured by a stationary observer is
[tex] L_r = L_o \sqrt{1 - \frac{v^2}{c^2 } cos^2(\theta ) }[/tex]
Generally the angle made is mathematically represented
[tex]tan(\theta) = \frac{L_y}{L_x}[/tex]
=> [tex]tan {\theta } = \frac{L_o sin(\theta )}{ (L_o cos(\theta ))\sqrt{ 1 -\frac{v^2}{c^2} } }[/tex]
=> [tex]tan(\theta ) = \frac{tan\theta}{\sqrt{1 - \frac{v^2}{c^2} } }[/tex]
Explanation:
The special relativity relations allow to find the results for the questions about the measurements made by an observed at rest on the rod are:
a) The length of the rod is: [tex]L = L_o \sqrt{1 - \frac{v^2}{c^2} \ cos^2\theta_o }[/tex]
b) The angle with respect to the x axis is: [tex]tan \theta = \frac{tan \theta_o}{\sqrt{1- \frac{v^2}{c^2} } }[/tex]
Special relativity studies the motion of bodies with speeds close to the speed of light, with two fundamental assumptions.
The laws of physics are the same in all inertial systems. The speed of light in vacuum has the same value for all inertial systems.
If we assume that the two systems move in the x-axis, the relationship between the components of the length are:
[tex]L_x = L_{ox} \ \sqrt{1- \frac{v^2}{c^2} }[/tex]
[tex]L_y = L_o_y \\L_z = L_{oz}[/tex]
Where the subscript "o" is used for the fixed observed on the rod, that is, it is at rest with respect to the body, v and c are the speed of the system and light, respectively.
a) They indicate that the length of the rod is L₀ and it forms an angle θ with the horizontal.
Let's use trigonometry to find the components of the length of the rod in the system at rest, with respect to it.
sin θ = [tex]\frac{L_{oy}}{L_o}[/tex]
cos θ = [tex]\frac{L_{ox}}{L_o}[/tex]
[tex]L_{oy}[/tex] = L₀ sin θ
L₀ₓ = L₀ cos θ
Let us use the transformation relations of the length of the special relativity rod.
x-axis
[tex]L_x = (L_o cos \theta_o) \ \sqrt{1- \frac{v^2}{c^2} }[/tex]
y-axis
[tex]L_y = L_{o} sin \theta_o[/tex]
The length of the rod with respect to the observer using the Pythagorean theorem is:
L² = [tex]L_x^2 + L_y^2[/tex]
[tex]L^2 = (L_o cos \theta_o\sqrt{1- \frac{v^2}{c^2} })^2 + (L_o sin \theta_o)^2[/tex]
[tex]L_2 = L_o^2 ( cos^2 \theta_o - cos^2 \theta_o \frac{v^2}{c^2} + sin^2\theta_o)[/tex]
[tex]L^2 = L_o^2 ( 1 - \frac{v^2}{c^2} \ cos^2 \theta_o)[/tex]
[tex]L= Lo \sqrt{1- \frac{v^2}{c^2} cos^2 \theta_o}[/tex]
b) the angle with the x-axis measured by the stationary observer is:
[tex]tna \theta = \frac{L_y}{L_x}[/tex]
[tex]tan \ theta = \frac{L_o sin \theta_o}{L_o cos \theta_o \sqrt{1- \frac{v^2}{c^2} } }[/tex]
[tex]tan \theta = \frac{tan \theta_o}{\sqrt{1-\frac{v^2}{c^2} } }[/tex]
In conclusion, using the special relativity relations we can find the results for the questions about the measurements made by an observed at rest on the rod are:
a) The length of the rod is: [tex]L = L_o \sqrt{1- \frac{v^2}{c^2} \ cos^2\theta_o }[/tex]
b) The angle to the x axis is: [tex]tan \theta = \frac{tan \theta_o}{\sqrt{1- \frac{v^2}{c^2} } }[/tex]
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Iu Metallic bonding is similar to iconic bonding because
Answer:
In an ionic bond the valence electrons are transferred from the metal
Explanation:
Which statements are true for two oppositely charged, isolated parallel plates: C=capacitance, U=stored energy (Q and -Q = charge on the plates). Note: Isolated plates can not lose their charge.
1. Inserting a dielectric decreases U.
2. When the distance is doubled, C increases.
3. Increasing the distance increases the Electric field.
4. Inserting a dielectric increases Q.
5. Inserting a dielectric increases C.
6. When the distance is halved, Q stays the same.
7. When the distance is doubled, U increases.
Answer:
Explanation:
1) True. The stored energy (U) is proportional to the electric field strength (E). The electric field strength decreases when a dielectric is introduced hence inserting a dielectric decreases U.
2) False. From the formula [tex]C=\frac{Q}{V}=\frac{Q}{Vd}[/tex], capacitance is inversely proportional to distance hence if the distance is doubled, capacitance decreases.
3) False. As the distance between the electric field and the object increases, its electric field decreases.
4) False. If a dielectric is inserted, the plates are further separated. Q stays the same.
5) True. The electric field strength decreases when a dielectric is introduced and capacitance is inversely proportional to electric field hence Inserting a dielectric increases C
6) True. If a dielectric is inserted, the plates are further separated. Q stays the same.
7) True. When the distance is doubled, U increases
While playing Quidditch you throw the quaffle straight down to the person below you at
a speed of 8.8 m/s. If your friend catches it after 0.19 seconds how fast will it be going?
Answer:
the ans will be because it has 1.672
What is the meaning of agility
Answer:
Agility or nimbleness is an ability to change the body's position efficiently, and requires the integration of isolated movement skills using a combination of balance, coordination, speed, reflexes, strength and endurance.
Explanation:
Hope this helps I don't know if this is what you were looking for?
A car is pushed and travels 12 m. The same car is then pushed and it travels 15m. What could of
happened? Select 2 answers.
The force was increased
The mass was decreased
The force was decreased
The mass was increased
Explanation:
The force was increased
What is the speed of an object that travels 12 meters in 3
seconds?
Answer:
4 meters per second
Explanation:
12 divided by 3 = 4
For a substance to change from a gas to a liquid what must happen to its particles
A. they must lose enough of their kinetic energy that their motion is influenced by the attractions between them
B. they must gain enough kinetic energy ti allow them to move freely while still being attracted to one another
C. They must lose enough of their kinetic energy so that the attractions between them hold in place as they vibrate
D. They must gain enough kinetic energy to break out of their ridged structure and move independently
For a substance to change from a gas to a liquid, its particles A. must lose enough of their kinetic energy that their motion is influenced by the attractions between them.
We want to know what change takes place when the particles of a substance that goes from gas to liquid. We need to consider that:
In a gas, the particles move freely, with great kinetic energy and the attraction forces between them are negligible.In a liquid, the particles have some degree of movement, although less than in the gas state and the attraction forces are higher.For a substance to change from a gas to a liquid what must happen to its particles:
A. they must lose enough of their kinetic energy so that their motion is influenced by the attractions between them. TRUE. The attraction between the molecules causes them to move less in the liquid state. B. they must gain enough kinetic energy to allow them to move freely while still being attracted to one another. FALSE. Liquids have lower kinetic energies than gases. C. They must lose enough of their kinetic energy so that the attractions between them hold in place as they vibrate. FALSE. Even though they must lose kinetic energy, they still have some left to move rather than just to vibrate. D. They must gain enough kinetic energy to break out of their ridged structure and move independently. FALSE. Liquids have lower kinetic energies than gases.For a substance to change from a gas to a liquid, its particles A. must lose enough of their kinetic energy that their motion is influenced by the attractions between them.
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Answer: A
Explanation:
A bird flew to catch a prey and went from 12 m/s to 22 m/s in 2 seconds. What was the magnitude of the bird's acceleration?
Answer: Peregrine falcons are famed for their high-speed, high-altitude stoops. Hunting prey at perhaps the highest speed of any animal places a stooping falcon under extraordinary physical, physiological, and cognitive demands, yet it remains unknown how this behavioural strategy promotes catch success. Because the behavioral aspects of stooping are intimately related to its biomechanical constraints, we address this question through an embodied cognition approach. We model the falcon’s cognition using guidance laws inspired by theory and experiment, and embody this in a physics-based simulation of predator and prey flight. Stooping maximizes catch success against agile prey by minimizing roll inertia and maximizing the aerodynamic forces available for maneuvering but requires a tightly tuned guidance law, and exquisitely precise vision and control.
Explanation:
Plastic is a good conductor of heat. True/ False
Answer:
false because they have no fee electrons
False, it is a poor conductor of heat. They are great insulators though.
Make sure to answer all questions that have not yet been answered Last/First Name (print): PHYS 1440-Section Username ID (XXX9999) WS Analysis A: 1. The voltage difference between the AA and AAA batteries should be quite small. What then might be the difference between them? AXAUUUUUU 2. If we have a resistor labeled brown-black-green-gold, what is the average expected value? Why is it necessary to measure the resistor? Analysis B: 3. What is the average voltage in step 8 of part B? And, when a DC offset is applied, what is the average voltage then? 4. What two values were obtained when calculating the root-mean-square voltage in step 13? How do they compare to the measured value? Which one is correct, and why? (Hint: with an offset Vrms = /DC +
Answer:
hello questions under analysis B are not complete hence I couldn't provide its answers
1)
AA batteries have more electrochemical composition AAA batteries are smaller AA batteries store more charges when compared with AAA batteries2) The average expected value is 1000 k ohms
Explanation:
1) The difference between AA and AAA batteries
some of the differences are
AA batteries have more electrochemical composition AAA batteries are smaller AA batteries store more charges when compared with AAA batteries2) The average expected value is 1000 k ohms
also it is necessary to measure the resistor because the actual value of resistance gotten from measurement is always different from the value obtained from color coding. also note that The last color band indicates the tolerance.
and the resistor given has Gold as its last color band
Define bond length using your own words
Answer:
the free encyclopedia. In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of the molecule.
Explanation:
What characterizes moral development in middle and late childhood? Give an Example?
Answer: what characterizes moral development in mid to late childhood is
People at this level of moral development base their decisions on what their parents and/or law enforcement says is right. Stage 3 is about social conformity. ... Stage 4 is all about law and order for all. For example, someone may think, 'If I steal, I will break the law and breaking the law is wrong.Feb 17, 2016
Explanation:
A race car driver travel 350 ft/s (250mph) for 20 seconds. How far did she travel?
What is Newton first law?
Newton's First Law of Motion states "An object continues to be in its state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force".
PLZ HELP!!!
Which of the following is a vector quantity?
Answer:
B 30 M down
Explanation:
In physics we have two types of quantities:
- Scalar quantity: it is a quantity which only has a magnitude (e.g: mass and time are scalar quantities, since they only have a magnitude)
- Vector quantity: it is a quantity which has both a magnitude and a direction (e.g: velocity is a vector quantity, since it has a magnitude (the speed) and a direction)
In this problem, we have:
A. 100 ounces of water --> scalar (this is a volume, which has only a magnitude)
B. 30 m down --> vector (this is a displacement, which has both a magnitude (30 m) and a direction (down)
C. 88 mi/s --> scalar (this is a speed, which has only a magnitude)
D. 45 gallons in a bucket --> scalar (this is a volume, which has only a magnitude)
So, the correct option is B.
credit to skyluke89
How do warm ocean currents affect the weather?
A. They make the equator warmer.
B. They make the tropical regions warmer.
C. They reduce precipitation in coastal areas.
D. They result in warmer air temperatures near the current.
If you get it right you get 100 points and a brainliest
Answer:
the answer is D I believe
Answer:
Answer: D
They result in warmer air temperatures near the current.
Explanation:
i took a test with the same question and got it right
Carlos is baking a cake. The last step in the directions is to put the cake batter in the oven. Why does Carlos need to put the cake in the oven?
A
The oven protects the batter while it changes into a cake.
B
The light from the oven makes it easy to see the batter change.
С
The oven is a place to put the cake so it has enough time to change.
D
The heat energy from the oven causes the batter to change into cake.
Answer:
D
Explanation:
I believe its D because A wouldn't really make sense, having to see the cake doesn't have anything to do with it changing so its not B, and C doesn't make sense because the time frame doesn't matter, D makes sense because it has to do with heat energy
The last step in the direction is to put the cake batter in the oven because the heat energy from the oven causes the batter to change into the cake.
What is Heat?A temperature difference causes energy to flow through one body to another, known as heat. Energy is transferred, or heat flows, when two bodies of differing temperatures are brought together. The hotter body goes to the cooler.
Typically, but not always, this energy transfer causes the temperature of a colder body to rise and the heat of the region of high temperature to fall.
Shifting from one physiological body (or phase) to another, such as melting from a solid to a liquid, sublimation from a solid to a vapor, boiling from a liquid to a vapor, or changing from one solid form to another, allows a substance to absorb heat without increasing in temperature.
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A frog is sitting on a lily pad when it sees a delicious fly. He darts out his tongue at a speed of 3.90 m/s to catch the fly. The tongue has a mass of 0.410 g, and the rest of the frog plus the lily pad have a mass of 12.5 g. What is the recoil speed of the frog and the lily pad? Ignore drag forces on the pad due to the water.
Answer:
Recoil speed of the frog and the lily pad, v₂ = 0.124 m/s
Explanation:
According to the law of conservation of linear momentum, in a closed system of colliding bodies, the momentum before collision is equal to the momentum after collision.
Momentum before collision = m₁v₁
momentum after collision = (m₁ + m₂)v₂
where m₁ = mass of the tongue; v₁ = velocity of the tongue; m₂ = mass of th frog and lily pad; v₂ = velocity of the frog and lily pad
m₁v₁ = (m₁ + m₂)v₂
v₂ = (m₁v₁)/(m₁ + m₂)
m₁ = 0.41 0 g = 0.00041 kg; v₁ = 3.90 m/s/; m₂ = 12.5 g = 0.0125 kg; v₂ = ?
v₂ = (0.00041 kg * 3.90 m/s)/(0.000410 + 0.0125 kg)
v₂ = 0.124 m/s
The following are examples of sources, except:
A. written letter
B. interview
C. Table of contents
D. photo
I'm pretty sure your answers are B, D, A
Consider a capacitor made of two rectangular metal plates of length and width , with a very small gap between the plates. There is a charge on one plate and a charge on the other. Assume that the electric field is nearly uniform throughout the gap region and negligibly small outside. Calculate the attractive force that one plate exerts on the other. Remember that one of the plates doesn't exert a net force on itself. (Enter the magnitude. Use any variable or symbol stated above along with the following as necessary: r0.)
F = θ/2∑0_w
Answer:
F= σ² L² /2ε₀
F = (L² ε₀/4π) ΔV² / r⁴
Explanation:
a) For this exercise we can use Coulomb's law
F = - k Q² / r²
where the negative sign indicates that the force is attractive and the value of the charge is equal to the two plates
Capacitance is defined by
C = Q / ΔV
Q = C ΔV
also the capacitance for a parallel plate capacitor is related to its shape
C = ε₀ A / r
we substitute
Q = ε₀ A ΔV / r
we substitute in the force equation
F = k (ε₀ A ΔV / r)² / r²
k = 1 / 4πε₀
F = ε₀ /4π L² ΔV² / r⁴4
F = L² ΔV² ε₀/ (4π r⁴)
F = (L² ε₀/4π) ΔV² / r⁴
b) Another way to solve the exercise is to use the relationship between the force and the electric field
F = q E
where we can calculate the field created by a plane using Gaussian law, where we use a cylinder with a base parallel to the plate as the Gaussian surface
Ф = ∫E .dA = [tex]q_{int}[/tex] / ε₀
the plate have two side
2E A = q_{int} / ε₀
E = σ / 2ε₀
σ = q_{int} / A
substituting in force
F = q σ / 2ε₀
the charge total on the other plate is
q = σ A
q = σ L²
F= σ² L² /2ε₀
An object is dropped from rest and falls freely 20 meters to Earth. When is the speed of the object 9.8 meters per second?
Answer:
at the end of its first second of fall
Explanation:
Can I have brainliest
The graph below was created from the motion of a cart on a ramp. Use the graph to answer the question that follows.
main seconde
What is the acceleration of the object at t4s?
A girl runs 120m due north in 15s. she then runs 80m due east in 12s.What is average speed?
The average speed of the girl is 2.26 m/s.
The average speed is calculated by dividing the total distance traveled by the total time taken. In this case, the girl traveled a total distance of 120 m + 80 m = 200 m. She took a total time of 15 s + 12 s = 27 s to travel this distance.
Therefore, the average speed is:
average speed = total distance / total time
average speed = 200 m / 27 s
average speed = 2.26 m/s
The average speed does not take into account the direction of the motion. The girl traveled in two different directions, so the average speed is not a meaningful measure of her speed.
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What is the objective of playing basagang palayok?the goal what is the goal of playing basang palayok
Answer:
Explanation:
At first glance, it looked like a group of kids-at-heart playing traditional Filipino games under the sun. But up close the games were played by public school teachers staging a unique protest to demand government to prioritize their welfare.
Some 100 members of the Teacher’ Dignity Coalition (TDC) from Metro Manila staged what they called “Palarong Pampista” at the Plaza Miranda in Manila yesterday to demand salary increases this year.
The protest is part of the “Protest de Mayo” launched by TDC earlier this month to call for a P10,000 across-the-board increase in salaries of government teachers and the scrapping of the performance-based bonus of the Aquino government which they described as “deceptive, unfair and divisive.”
During the protest, teachers played traditional fiesta games like Palo Sebo and Basagang Palayok “to demonstrate their sacrifices for the country despite the inadequate compensation from the government.”
TDC National Chairperson Benjo Basas said Palo Sebo and Basagang Palayok were symbols of how the government is treating public school teachers.
Palo Sebo, a popular fiesta game in which contestants climb a greased bamboo in order to get the money prize at the top, is the same as the government’s performance-based bonus or PBB, Basas said.
“It promises a cash prize, but teachers and employees need to fight and pull others down in order to be on top,” he explained.
The Basagang Palayok is also another popular fiesta game where the players’ objective is to hit the hanging pot with prizes. Basas said that in this game, “the player is blindfolded, and like the P10,000 salary increase demand, the prize is uncertain and the players must make all the effort and pass the obstacles.”
Earlier, Education Secretary Armin Luistro said that the Department of Education (DepEd) “recognizes the right of our teachers to raise their concerns publicly.”
“We will not object to any measure that will help public school teachers,” said Luistro. “As long as there is adequate funding, a raise in teachers’ salaries will be welcome,” he said.
However, while DepEd expressed support to the plight of public school teachers for salary increase, Luistro enjoined “certain groups not to take any action that greatly affects the delivery of basic services to our learners.”
TDC, a 30,000-strong group, has set several other unique mass actions until the resumption of classes in June 2 in all public elementary and secondary schools nationwide.
The goal of playing basang palayok is successfully smashes the palayok (clay pot)
basang palayok its a Filipino traditional fun game played during fiestas and birthday parties. For this game the following objects are necesary
Palayok (clay pot) Candies, coins or chocolates Small pieces of colorful paper Flour Rope
Then the palayok is filled with sweets, coins, flour, chocolates and colored paper and later suspended with the rope in the air by trying it on a branch of a tree traditionally a Mango tree.
Then a player will be blindfolded and then spins around close to ten times to disorient him/her. After that, the player will be given a bamboo pole as commonly used to hit the pot.
In that moment, the game starts and the crowd shouts out instructions to the player such as "go straigh, to the left, to the right, stop" and the player get on attempt to hit it hard enough to break the clay pot.
If he/she does not break the pot, another guest at the party gets his/her turn If he breaks it everyone in the crowd goes for the goodiesFinally, the player who successfully smashes the palayok is given a prize.
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How does the eccentricity of a typical cometary orbit compare to that of a typical planet
Answer:
Explanation:
Comets are balls of ice and dust in orbit around the Sun. The orbits of comets are different from those of planets - they are elliptical. A comet's orbit takes it very close to the Sun and then far away again.
What would the kinetic energy and potential energy be with the snowboarder, before during and after a jump?
Answer: Before the jump, the snowboarder would carry potential energy.
During the jump he will carry kinetic energy.
And after the jump, assuming hes at a full stop, he will carry potential energy once again.
Answer:
Before the jump, the snowboarder would carry potential energy.During the jump he will carry kinetic energy.And after the jump, assuming hes at a full stop, he will carry potential energy once again. Explanation:
Find the weight of a pumpkin hanging from two scales, if scale one reads 55 N, scale two reads 58 N, and the angle θ between the strings coming from the two scales is 121 degrees.
Answer:
The weight of the pumpkin is 46.793 newtons.
Explanation:
We consider the string-pumpkin system as our system, in which weight of pumpkin create two distinct tensions through cords. The equations of equilibrium are now described:
[tex]\Sigma F_{x} = -T_{1}\cdot \sin \theta_{1}+T_{2}\cdot \sin \theta_{2} = 0[/tex] (Eq. 1)
[tex]\Sigma F_{y} = T_{1}\cdot \cos \theta_{1}+T_{2}\cdot \cos \theta_{2} -W = 0[/tex] (Eq. 2)
Where:
[tex]T_{1}[/tex], [tex]T_{2}[/tex] - Tension through cords, measured in Newtons.
[tex]W[/tex] - Weight of the pumpkin, measured in Newtons.
[tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex] - Inclination of each cord with respect to the vertical, measured in sexagesimal degrees.
If we know that [tex]T_{1} = 55\,N[/tex], [tex]T_{2} = 58\,N[/tex], [tex]\theta_{1} = \theta[/tex] and [tex]\theta_{2} = 121^{\circ}-\theta[/tex], the system of equations becomes:
[tex]-55\cdot \sin \theta +58\cdot \sin (121^{\circ}-\theta) = 0[/tex] (Eq. 1b)
[tex]55\cdot \cos \theta + 58\cdot \cos (121^{\circ}-\theta) = W[/tex] (Eq. 2b)
From Trigonometry, we remember the following identity:
[tex]\sin (121^{\circ}-\theta) = \sin 121^{\circ}\cdot \cos \theta -\cos 121^{\circ}\cdot \sin \theta[/tex]
[tex]\sin (121^{\circ}-\theta) = 0.857\cdot \cos \theta -0.515\cdot \sin \theta[/tex] (Eq. 3)
By applying (Eq. 3) in (Eq. 1b), we get the following expression after expanding and simplifying algebraically:
[tex]-55\cdot \sin \theta + 58\cdot (0.857\cdot \cos \theta - 0.515\cdot \sin \theta) = 0[/tex]
[tex]-84.87\cdot \sin \theta +49.706\cdot \cos \theta = 0[/tex]
And we solve the equation for [tex]\theta[/tex]:
[tex]\tan \theta = \frac{49.706}{84.87}[/tex]
[tex]\theta = \tan^{-1} 0.585[/tex]
[tex]\theta \approx 30.328^{\circ}[/tex]
Then, the weight of the pumpkin is: ([tex]\theta \approx 30.328^{\circ}[/tex])
[tex]W = 55\cdot \cos 30.328^{\circ}+58\cdot \cos (121^{\circ}-30.328^{\circ})[/tex]
[tex]W = 46.793\,N[/tex]
The weight of the pumpkin is 46.793 newtons.
The weight of the pumpkin hanging from the two scales is 98.36 N.
The given parameters;
reading on scale one, a = 55 Nreading on scale two, b = 58 Nangle between the two scales, θ = 121⁰The weight of the pumpkin hanging from the two scales is equal to the resultant of the two scale readings.
The resultant of the two force is calculated as follows;
R² = a² + b² - 2abcos(θ)
R² = 55² + 58² - 2(55)(58)cos(121)
R² = 9674.7
[tex]R = \sqrt{9674.7} \\\\R = 98.36 \ N[/tex]
Thus, the weight of the pumpkin hanging from the two scales is 98.36 N.
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11)A 1100 kg car travels on a straight highway with a speed of 30 m/s. The driver sees a red light ahead and applies her
brakes, which exert a constant braking force of 4000N. In how many seconds will the car stop?
Answer:
Time taken = 8.25 second
Explanation:
Given:
Force = 4000 N
Force = ma
4,000 = (1100)(a)
Acceleration = 3.6363 m/s²
v = u + at
0 = 30 + (3.6363)t
Time taken = 8.25 second
The time taken by the car to stop is 8.26 s.
Given data:
The mass of car is, m = 1100 kg.
The speed of car is, u = 30 m/s.
The magnitude of braking force is, F = 4000 N.
We need to first obtain the acceleration of car to get that, apply the Newton's second law as,
F = - ma (Negative sign shows that the force will resist the motion)
4000 = -(1100) a
[tex]a =-\dfrac{4000}{1100}\\\\a =-3.63 \;\rm m/s^{2}[/tex]
Now, apply the first kinematic equation of motion to obtain the time taken by the car to stop as,
v = u + at
Here, v is the final speed and v = 0, since car will stop finally.
So,
[tex]0=30+(-3.63)t\\\\t = \dfrac{30}{3.63}\\\\t=8.26 \;\rm s[/tex]
Thus , we can conclude that the time taken by the car to stop is 8.26 s.
Learn more about the Newton's second law of motion here:
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If an airplane needs a minimum of 148 m/s to take off, and it accelerates at 3 m/s^2, how long should the runway be so that it can take off at this minimum speed?
Assuming it takes off from rest, the runway should have length x such that
(148 m/s)² - 0² = 2 (3 m/s²) x
which follows from the formula,
v² - u² = 2 a ∆x
(where u is initial speed and v is final speed; the other two's significance should be obvious)
Solve for x :
x = (148 m/s)² / (2 (3 m/s²))
x ≈ 3650.67 m