You swing a bat and hit a heavy box with a force of 1500 n. the force the box exerts on the bat is

Answers

Answer 1
Exactly 1500 N whether or not the box moves.

Related Questions

Bob is studying waves in science and learns that the energy of a wave is directly proportional to the square of the waves amplitude. If the amplitude of a wave changes from 2m to 1m, what should he predict as the effect on energy of the wave? A) The energy is halved. B) The energy is doubled. C) The energy is quartered. D) The energy is quadrupled.

Answers

For a simple harmonic motion energy is given with:
[tex]E=\frac{1}{2}kA^2[/tex]
Where k is a constant that depends on the type of the wave you are looking at and A is amplitude.
Let's calculate the energy of the wave using two different amplitudes given in the problem:
[tex]E_1=\frac{1}{2}k(1)^2=\frac{1}{2}k\\E_2=\frac{1}{2}k(2)^2=\frac{4}{2}k=2k\\[/tex]
We can see that energy associated with the wave is 4 times smaller when we decrease its amplitude by half. So the answer should be C.


Answer:

It's C

Explanation:

Since E ∝ amplitude2 then as the amplitude is halved the energy is quartered.

Plugging in to check

amplitude2=E

22=4

12=1

Volume or intensity of a sound wave is measured by the size of the _________ and reported in decibels.

Answers

The answer would be; Amplitude.

Hope that helps! :-)

Answer:

Amplitude

Explanation:

The intensity (or volume) of a sound wave is proportional to the square of the sound wave:

[tex]I\propto A^2[/tex]

where A is the amplitude of the wave.

The amplitude of a sound wave is measured as the maximum displacement of the wave with respect to its equilibrium position.

The intensity is measured in Decibels (dB), which is related to the logarithmic ratio between the power of two different sounds, i.e. the difference in decibels between two sounds is given by

[tex]10 Log (\frac{P_2}{P_1})[/tex]

where P1 and P2 are the power of the two sounds.

A rotating fan completes 1100 revolutions every minute. consider a point on the tip of a blade, at a radius of 0.18 m. through what distance does the point move in one revolution?

Answers

We don't need the angular speed to solve this exercise. In fact, the distance covered by the point in one revolution corresponds to one circumference of radius r, with r being the radius at which the point is located. Therefore, the distance covered by the point in one revolution is
[tex]d=2 \pi r = 2 \pi (0.18 m)=1.13 m[/tex]

Sally and Maria were running around the track during PE. They were not happy and decided to stop and rest once they got to the bleachers. After a 10 minute rest, they started running again, but Sally tripped and fell. At what time during their run did Sally fall for a minute? A) at 4 minutes B) at 14 minutes C) at 15 minutes D) at 20 minutes

Answers

Answer:

The answer is A.) 4 minutes

Explanation:

If you look at the graph they started at 15  and when they took a rest it was at 4 mins.

Answer:

B)15 Minutes

The line becomes straight for one min at the fifteen min marker.

Hope this helps

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What vibrates when an aeroplane flies over our house?

Answers

The Anser is molecules from the air

The sound that airplane products transport through molecules of air gases into space, in a way that air molecules oscillate. The oscillation of the molecules from the air is transferred to the structure of a building and it begins to vibrate as well.

You probably have noticed that, as you increase ω, there will be a value, ωcrit, for which r(ω) goes to infinity. find ωcrit. answer in terms of k and m.

Answers

For the mass m, attached to a spring, to move in a circle centripetal force and restoring force of the spring must be equal. Centripetal force is given with this formula:
[tex]F_c=\frac{mv^2}{r}=\frac{mw^2r^2}{r}=mw^2r[/tex]
Restoring force only occurs if the spring is stretched. If L is the length of unstretched spring we have the following formula for restoring force:
[tex]F=k(r-L)[/tex]
r is the length of a circle that mass m is traveling along. 
As said above, these two forces have to be equal:
[tex]F=k(r-L)=mw^2r[/tex]
We solve for r:
[tex]F=k(r-L)=mw^2r\\ kr-kL=mw^2r\\ mw^2r-kr=-kL\\ r(mw^2-k)=-kL\\ r=\frac{-kL}{mw^2-k}\\ r(w)=\frac{kL}{k-mw^2} [/tex]
r(w) will go to infinity when denominator is equal to zero:
[tex]k-mw^2=0\\ k=mw^2\\ w^2=\frac{k}{m}\\ w_{crit}=\sqrt{\frac{k}{m}}[/tex]
Please keep in mind that Hooke's law has it's limitations, and before we reach our critial value of angular velocity spring will be strecthed to a point where Hooke's law does not aply anymore.

If a 70-kg swimmer pushes off a pool wall with a force of 250 N what is her acceleration

Answers

F= MA 
force equals mass time acceleration 
250 N = (70 kg ) (A)
250/70 = 3.5 which is about 4 m/s 
Hope this helps

Why is the thickness greater for the bass strings of a guitar than for the treble strings?

Answers

Thick strings have greater inertia, so they will be more resistant to vibrating.

The equation of motion of a particle is s = t3 â 27t, where s is in meters and t is in seconds. (assume t ⥠0.) (a) find the velocity and acceleration as functions of t.

Answers

Final answer:

To find the velocity and acceleration of a particle as functions of time in a given equation of motion, differentiate the equation with respect to time. The velocity function is v = 3t² - 27 and the acceleration function is a = 6t.

Explanation:

Velocity: To find the velocity, differentiate the equation of motion with respect to time which gives v = ds/dt. In this case, v = 3t² - 27.

Acceleration: Similarly, differentiate the velocity equation with respect to time to find acceleration, which results in a = dv/dt. Here, a = 6t.

After watching an advertisement for hand sanitizer on television, Ben decided to see just how effective the advertised hand sanitizer really was. Ben used warm water as his control. He compared the advertised sanitizer with two brands of hand soap. In all four trials he rubbed his hands together for two minutes. After using the three products and the control, he cultured the bacteria on his hands. He recorded the number of bacterial cultures that appeared on each culture plate. Ben's results can be seen in the data table. Ben concluded that both brands of soap were more effective in killing bacteria than the advertised hand sanitizer. What term BEST describes Ben's results for all four trials? A) biased B) inconclusive C) qualitative D) quantitative ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

answer is quantitive this guy is wrong

Explanation:

did it on usatestprep

18. In a solid conductor such as a metal, what is the cause of an electric current? A. A flow of positive and negative charges. B. A flow of positive charges only. C. +A flow of negative charges only. D. A flow of protons. E. A flow of neutrons.

Answers

The answer is A.  A flow of positive and negative charges.

6. You stopped swimming laps to take a 10 second quick count and counted 25 beats. Explain how to find your beats per minute.

Answers

If you stopped for ten seconds you would just multiply 25 by 6 because each minute is 60 seconds. 

If you stop swimming laps to take a count to 10 seconds then, and you counted for 25 beats, then that is 150 beats per minute.

What is unit conversion?

Conversion of units is defined as the process of multiplying or dividing different units and measurements of the same quantity. Conversion is the process of transforming the value of one form to another, such as inches to millimeters or liters to gallons in mathematics. Units are used to calculate length, weight, capacity, temperature, and speed.

Now, according to the question, the best way to solve the question is,

If you paused for ten seconds, simply multiply 25 by six because each minute equals 60 seconds.

When you multiply the 25 beats to 60 seconds, the answer you get is 150 beats per second.

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give the reason why the horizontal component of the velocity of a projectile remains the same at every point of its flight

Answers

Because ...

-- If you ignore air resistance ... which we always do for these problems ... then there's NO horizontal force acting on the projectile.

-- Since there's no horizontal force on the projectile, its horizontal acceleration is zero.

-- Since the projectile has no horizontal acceleration, the horizontal component of its velocity is constant. 

Match the cloud type with its description.




1.
cumulus
resembles an overcast sky; layers of gray or white clouds

2.
altostratus
clouds nearest Earth's surface

3.
cirrus
look like wispy feathers high in the sky

4.
nimbostratus
dark, thick-layered clouds; rain's coming

5.
fog
look like pieces of cotton in the sky

Answers

Cumulus clouds are easy to distinguish because they look like piles of cotton. They have rounded edges. The Latin word 'cumulus," is loosely translated as "heap," in English. 

Altostratus are mid-level clouds that resemble an overcast sky. Predominantly grey, they spread out widely and is usually associated with light rain. It can morph into a nimbostratus, which are clouds that carry heavy rain.

Cirrus clouds are thin and wispy. They are high-level clouds that often appear bright yellow just as the sun rises and red after the sun sets. 

Nimbostratus clouds are dark thick-layered clouds. "Nimbus," is Latin  which means rain and "stratus," means spread-out. 

Fog are clouds nearest to the surface. They are also called stratocumulus clouds. These are stratus clouds that form near the ground. 

The highest element in the hierarchical breakdown of the wbs is

Answers

Work package. Hope this helps!
Final answer:

The highest element in the hierarchical breakdown of the Work Breakdown Structure (WBS) is the project itself. This project is then divided into definable and measurable tasks or subtasks forming a hierarchical structure.

Explanation:

The highest element in the hierarchical breakdown of the Work Breakdown Structure (WBS) is the project itself. WBS is a tool used in project management to divide a project into manageable chunks or portions. It begins with the final deliverable or project at the top level. This is subsequently broken down into definable and measurable tasks or subtasks forming a multi-level structure. A good example could be a software development project. The entire project would be the highest element and might be divided into phases like planning, design, coding, testing, and implementation. Each of these could be further broken down into more specific tasks.

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You exert a horizontal force on a heavy piano that rests on a carpeted floor. the piano doesn't budge. if the force you exert on the piano is the "action", what force is its reaction?

Answers

the force the piano exerts on you!

Answer:

it will cruch you so the piano exerts on you

Explanation:

The period of a mechanical wave is 4 seconds. What is the frequency of the wave? 8.0 waves/second 4.0 waves/second 0.25 waves/second depends on the speed of the wave

Answers

The formula for finding the frequency of a wave is with the following formula:
F = 1/T, F being the variable for frequency and T substituting as time. Given we already have our time, let's plug it in for T.
F = 1/4. This means our answer is in some mathematical form that is equivalent to 1/4. We have the answer "0.25 waves/second", which is equivalent to our original fraction (0.25 x 4 = 1.00).

I hope this helps!

Hello!

Data:

T (period) = 4 s

f (frequency) = ? (waves/second)  

Formula:

[tex]f = \dfrac{1}{T}[/tex]

Solving:

[tex]f = \dfrac{1}{T}[/tex]

[tex]f = \dfrac{1}{4}[/tex]

[tex]\boxed{\boxed{f = 0.25\:waves/second}}\end{array}}\qquad\quad\checkmark[/tex]

___________________________

I Hope this helps, greetings ... Dexteright02! =)

El Sol está en promedio a 93 millones de millas de la Tierra. ¿A cuántos metros equivale esto? Expréselo usando potencias de diez.

Answers

Final answer:

La distancia promedio entre la Tierra y el Sol es de aproximadamente 93 millones de millas. En metros, esta distancia es de aproximadamente 1.5*10^11. Se utiliza la notación científica 1.5 × 10¹¹ metros para representar esta distancia de forma más concisa y manejable.

Explanation:

El Sol está, en promedio, a 93 millones de millas de la Tierra. Sabemos que 1 milla equivale a 1.60934 kilómetros y que un kilómetro es igual a 10^3 metros. Por lo tanto, podemos decir que una milla es igual a 1.60934*10^3 metros.

Para convertir la distancia desde la Tierra hasta el Sol a metros, multiplicamos 93,000,000 millas por 1.60934*10^3 metros/milla. Esto da como resultado aproximadamente 1.5*10^11 metros. Así que, en notación científica, la distancia desde la Tierra hasta el Sol es de aproximadamente 1.5 × 10¹¹ metros.

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Positive psychologists believe that happiness can be increased by

Answers

Final answer:

Positive psychologists believe that happiness can be increased by various strategies and interventions, including practicing gratitude, engaging in acts of kindness, cultivating positive relationships, finding meaning and purpose in life, setting and achieving goals, and focusing on one's strengths and virtues. Research has shown that these activities and mindsets can enhance happiness and well-being. CBT and positive psychology interventions have also been found to be effective in increasing happiness and improving overall well-being.

Explanation:

Positive psychologists believe that happiness can be increased by various strategies and interventions. These include practicing gratitude, engaging in acts of kindness, cultivating positive relationships, finding meaning and purpose in life, setting and achieving goals, and focusing on one's strengths and virtues.

Research has shown that these activities and mindsets can enhance happiness and well-being. For example, studies conducted by Seligman and Lyubomirsky have demonstrated that practicing gratitude and performing acts of kindness can boost happiness levels.

Furthermore, interventions such as cognitive-behavioral therapy (CBT) and positive psychology interventions (PPIs) have been found to be effective in increasing happiness and improving overall well-being.

Final answer:

Positive psychologists believe that happiness can be increased by cultivating and focusing on positive affect and emotions.

Explanation:

Positive psychologists believe that happiness can be increased by cultivating and focusing on positive affect and emotions. This means intentionally seeking out activities and experiences that bring joy, gratitude, contentment, and other positive emotions. Research has shown that practicing gratitude, engaging in acts of kindness, forming strong social connections, setting and achieving meaningful goals, and finding purpose and meaning in life are all ways to increase happiness

When sodium reacts with chlorine, sodium chloride is produced. Andrew represented this reaction with this equation:


Na + Cl2 → 2NaCl


The equation is (BLANK 1) because the number of (BLANK 2) atoms is (BLANK 3) on both sides of the arrow.


BLANK 1

A) Balanced

B) Not Balanced


BLANK 2

A) Chlorine

B) Sodium


BLANK 3

A) Equal

B) Not Equal

Answers

Answer:

The equation is (NOT BALANCED) because the number of (SODIUM) atoms is (NOT EQUAL) on both sides of the arrow.

Explanation:

1) As per the Dalton theory (or mass conservation law) in a chemical reaction the atoms do not dissapear or appear but are conserved.

2) So the number of atoms of the elements in the reactants must be equal to the atoms of the elements of the products.

3) Balancing a chemical reaction is the mathematical process of equalling the atoms of each element on both sides of the reaction.

4) In the given chemical equation, the coefficent in front Na on the left side is 1 meaning that there is 1 atom of Na, while in the right side (the side of the products) the coefficient in front of NaCl is 2, meaning that there are 2 atoms of Na. So, the equation is not balanced.

The balanced equation is:

2Na + Cl2 --> 2NaCl

A car slows down from 27.7 m/s to 10.9 m/s in 2.37s. What is the acceleration?

Answers

acceleration = ( final velocity - initial velocity) / time taken

= (10.9-27.7) / 2.37

= - 7.088 m/s2

A car slows down from 27.7 m/s to 10.9 m/s in 2.37s.Then the acceleration is  -7.09 m/sec².

What is acceleration ?

Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration.

An object has positive acceleration if it is accelerating and travelling in the right direction. Positive acceleration was demonstrated in the first example by the speeding car. The acceleration is occurring in the same direction as the car's motion, which is forward and speeding up.

The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t).

The final velocity 'v' =10.9 m/s

The time 't' = 2.37 secs.

Then acceleration = -7.09 m/sec² or, decceleration is 7.09 m/sec².

Thus, the acceleration is  -7.09 m/sec².

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a chandelier weighing 100 newtons is suspended by two wires that make an angle of 60° with the ceiling. Find the tension in both wires.
58 newtons
87 newtons
116 newtons
231 newtons

Answers

Number A. 58 N 

See pictures below

An eagle that has a mass of 4.5 kg is spotted 5 m above a lake

Answers

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
 PLEASE SEE ATTACHED IMAGE.

 By definition, the potential energy is given by:
 Ep = m * g * h
 Where,
 m: mass
 g: gravity
 h: height.
 The potential energy change is:
 Delta Ep = Epf- Epi
 Delta Ep = m * g * hf - m * g * hi
 Delta Ep = m * g * (hf - hi)
 Substituting values:
 Delta Ep = (4.5) * (9.8) * (25 - 5)
 Delta Ep = 882 J
 Answer:
 the eagle gain: 
 Delta Ep = 882 J

An Eagle that has a mass of 4.5 kg is spotted 5 m above a lake. It flies up to its nest in a tree at a height of 25 m.  How much gravitational potential energy did the eagle gain?

This is the original question

Answer:

882 J = PEg = MGH     M = mass in Kg   G = 9.6 m/s     H = height

Height in this case is the displacement (25m - 5m) = 20m

Hope this helps.

to cook food in the microwave oven converts electrical energy into. energy. a. electricmagnetic. b. heat. c. mechanical d.nulcleae

Answers

To cook food in the microwave oven converts electrical energy into A.  electric magnetic.
hello
its A because of heat and u have to plug the cord in ands et the time
have a nice day

Sugar mixed in water is an example of a _______________ .


A colloid
B suspension
C pure substance
D solution
E heterogeneous mixture

Answers

Sugar water is a solution and not a colloid. Solutions are homogeneous mixtures of two or more components. In a solution, the substance is dissolved in the solute. Sugar water is a solution and not a colloid. Solutions are homogeneous mixtures of two or more components.

Answer:

option D is correct. It is a solution.

Explanation:

A physical change occurs when sugar dissolves in water. It is due to the fact that no new substance is formed.the process is reversible.as sugar is solute.water is solvent.What is solute?

A solute is a substance that dissolves in a solution. A solvent and one or more solutes make up every solution.

hence, option D is correct. It is a solution.

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A light train made up of two cars is traveling at 90 km/h when the brakes are applied to both cars. know that car a has a mass of 30 mg and car b has a mass of 20 mg, and the braking force is 40 kn on each car.

Answers

Missing questions in the text:
"determine (a) the distance traveledby the train before it comes to a stop (b) the coupling force between the cars as the is slowing down."
Note: The masses of the car are in Mg, not mg.

Solution:

(a) To find the solution of this part, we should write that the resultant of the forces acting on the x-axis (horizontal plane) is equal to the product between the total mass of the system (the mass of the two cars) and the acceleration (Second Newton law).
The only force acting on the light train system is the force of the brakes, Fb=40 kN = 40000 N, multiplied by 2 because it acts on both cars. The masses of the two cars are [tex]m_A=30 Mg=30000 Kg[/tex] and [tex]m_B = 20 Mg=20000 Kg[/tex], therefore Newton's law becomes
[tex](m_A+m_B) a = -2F_b[/tex]
where the negative sign in front of Fb means the force is acting against the direction of the motion. Solving for a, we find
[tex]a= \frac{-2 F_b}{m_A+m_B}= \frac{-2 \cdot 40000 N}{50000 Kg}=-1.6 m/s^2 [/tex]
where the negative sign means the light train is decelerating.
Once we find a, we can find the total distance covered by the train. We know the initial velocity, vi=90 km/h=25 m/s, the final velocity (0 m/s) and the acceleration, so we can use:
[tex]2aS=v_f^2-v_i^2=-v_i^2[/tex]
From which we find
[tex]S= \frac{v_i^2}{2a}=195.3 m [/tex]

(b) To solve this part of the problem, let's write Second Newton's law with the forces acting only on the car A. We have only two forces: the force of the brake, Fb, and the coupling force, Fc. So we can write
[tex]m_A a = F_c-F_b[/tex]
And so
[tex]F_c =m_A a+F_b=30000 Kg \cdot (-1.6 m/s^2)+40000 N = -8000 N[/tex]
Where once again, the negative sign means that Fc is against the direction of the motion.
Final answer:

The Physics related question involves concepts of Newton's Third Law and momentum. When brakes are applied, a force is exerted against the car's motion. The impact differs based on the car's mass, and its initial momentum which is the product of its mass and velocity.

Explanation:

The subject of the question is related to Physics, specifically focusing on the topic of Newton's laws of motion and momentum. To understand the scenario, we should first comprehend that when the brakes are applied to the cars, a force is exerted which slows them down. This relates to Newton's Third Law - for every action, there's an equal and opposite reaction.

Considering the given scenario, when the brakes apply a force of 40 kN on each car, this force works against their forward momentum, slowing them down. The impact of the force will differ based on the mass of each car, with the lighter car likely slowing down faster than the heavier one. This can be calculated if we know the exact measure of force and the braking distance.

Additionally, the momentum of the cars before the brakes are applied could also be calculated using the formula momentum = mass x velocity, which in this case would have different results for each car due its mass difference, despite identical velocities. Overall, the problem illustrates how both the Newton's third law and principles of momentum come into play in everyday physics scenarios like that of braking cars in motion.

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what type of simple machine is a catapult?( incline plane , lever , pulley , screw , wedge, or a wheel and axle) How do you know ?

Answers

Answer: Lever

Explanation:

A catapult as a machine is a lever (1st class) because the fulcrum is between the Effort applied and the load(object) to be launched. A first class lever machine is a machine that has the fulcrum in between the effort and the load which makes a catapult a first class lever.

The handle of the catapult is where the effort is applied, the fulcrum is the point of contact between the rubber tied to the stick and the stick itself and the load is the object to be launched.

A catapult is a type of lever because it uses a rigid arm that pivots around a fixed point to launch a projectile.

A simple machine known as a lever is made up of a rigid bar or board that pivots around a fixed point, also known as a fulcrum. The fulcrum of a catapult is the location where the weapon's arm is joined to the base.

Potential energy is stored in the system when the catapult's arm is retracted. Potential energy is transformed into kinetic energy when the arm is released, which causes the arm to swing forward and fire the projectile.

Seesaws, scissors, and crowbars are a few examples of machines that utilize the lever concept. The lever enables the application of a little force over a longer distance to produce a bigger force over a shorter distance.

Therefore, a catapult is a type of lever. The correct answer is lever. An example of a lever is a catapult.

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Consider the vector b⃗ with magnitude 4.00 m at an angle 23.5∘ north of east. what is the x component bx of this vector? express your answer in meters to three significant figures.

Answers

Decomposing the vector b on the x-axis and the y-axis, we get a rectangle triangle where the two sides are bx (x-axis) and by (y-axis), and b is the hypothenuse.
The component in x, bx, is equal to the product between the hypothenuse and the cosine of the angle between b and the x-axis, which is [tex]23.5 ^{\circ}[/tex]:
[tex]b_x = b \cos (23^{\circ})=(4.00 m)(\cos (23^{\circ}))=3.68 m[/tex]

which of the following statements applies to current?
a. it is the flow of electric charge
b. it is measured in ohms
c. it is an excess accumulation of charge
d. it is made of neutrons

Answers

The answer is A. it is the flow of electric charge. Current in electric circuits is carried by moving electrons in a wire. The current can also be carried by ions in electrolyte. Ampere is the SI unit for measuring an electric current. The electric current is measured using an equipment called ammeter.

Answer:A

Explanation:

Find the magnitude of a fourth force on the stone that will make the vector sum of the four forces zero.

Answers

100cos30° + 80cos120° + 40cos233° + Dx = 0 
Dx = -22.53 N 

y components: 
100sin30° + 80sin120° + 40sin233° + Dy = 0 
Dy = -87.34 N 

magnitude of D: 
sqrt[(-22.53)² + (-87.34)²] 
90.2 N 

direction of D: 
arctan[(-87.34)/(-22.53)] 
75.5° ref, but since Dx and Dy are both negative, we know this vector is in QIV: 
360 - 75.5° = 284.5°

The magnitude of the fourth force will be 90.1956 N and the angle will be 75.535° made from the horizontal in the first quadrant.

Given to us

Force A, [tex]F_A = 100\ N[/tex]Angle made by Force A from the horizontal, [tex]\theta_A = 30^o[/tex]Force B, [tex]F_B = 80 \ N[/tex]Angle made by Force B from the Vertical, [tex]\theta_B = 30^o[/tex]Force C, [tex]F_C = 40 \ N[/tex]Angle made by Force C from the Horizontal, [tex]\theta_C = 53^o[/tex]

For Angle made by Force B,

As the angle given to us is from the vertical axis, we will make it from the horizontal,

[tex]\theta_B = (90^o -30^o) = 60^o[/tex]

Now, the magnitude of a fourth force on the stone should make the vector sum of the four forces zero. therefore,

[tex]\sum F_{horizontal} = 0[/tex]

[tex]F_A Cos(\theta_A) -F_B Cos(\theta_B) -F_C Cos(\theta_C) = F_{Dh}[/tex]

[tex]100 Cos(30^o) -80Cos(60^o) -40Cos(53^o) = F_{Dh}\\\\F_{Dh} = 22.5299\ N[/tex]

[tex]\sum F_{Vertical} = 0[/tex]

[tex]F_A Sin(\theta_A) +F_B Sin(\theta_B) -F_C Sin(\theta_C) = F_{Dv}[/tex]

[tex]100 Sin(30^o) +80Sin(60^o) -40Sin(53^o) = F_{Dv}\\\\F_{Dv} =87.3365\ N[/tex]

Resultant Force

[tex]R = \sqrt{(F_{Dh})^2+(F_{Dv})^2}\\\\R = \sqrt{(87.3365)^2+(22.5299)^2}\\\\R = \sqrt{7627.6642+507.5963}\\\\R = \sqrt{813526}\\\\R = 90.1956\ N[/tex]

The angle of the resultant,

[tex]Tan (\theta_D) = \dfrac{F_{Dv}}{F_{Dh}}\\\\Tan(\theta_D) = \dfrac{87.3365}{22.5299}\\\\Tan(\theta_D) = 3.87647\\\theta_D = Tan^{-1} 3.87647\\\theta_D =75.535^o[/tex]

Hence, the magnitude of the fourth force will be 90.1956 N and the angle will be 75.535° made from the horizontal in the first quadrant.

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