Answer:
what do u want to ask ????
A cylinder of compressed gas is at a temperature of 23 degrees. It is cooled until it reaches the pressure of 2000kPa. It has to be cooled to 90K before this happens. Calculate the starting pressure of the gas
Complete question is;
A cylinder of compressed gas is at a temperature of 23°C. It is cooled until it reaches the pressure of 2000kPa. It has to be cooled to 90K before this happens. Calculate the starting pressure of the gas
Answer:
Starting pressure = 604 KPa
Explanation:
We are given;
Initial temperature; T1 =23°C = 298 K
Final temperature; T2 = 90 K
Final pressure; P2 = 2000 KPa
From gay lussac's law, we know that;
P1•T1 = P2•T2
P1 = (P2•T2)/T1
P1 = (2000 × 90)/298
P1 ≈ 604 KPa
a motorcyclist drives from A to B with a uniform speed of 30 km/h and returns back with a speed of 20km/h-¹ find the average speed ?
PLEASE DO IT AS FAST YOU CAN AND NO SCAM ANSWERS OR ELSE I WILL REPORT
Answer:
Average speed = 24 km/h
Explanation:
Let the distance be x.Given the following data;
Uniform speed A = 30 km/h
Uniform speed B = 20 km/h
To find the average speed;
Mathematically, the average speed of an object is given by the formula;
[tex] Average \; speed = \frac {total \; distance}{total \; time} [/tex] ..... equation 1
Total time = TA + TB
[tex] T_{A} = \frac {x}{30} [/tex]
[tex] T_{B} = \frac {x}{20} [/tex]
[tex] Total \; time = \frac {x}{30} + \frac {x}{20} [/tex]
[tex] Total \; time = \frac {5x}{60} [/tex]
Total distance = x + x
Total distance = 2x
Substituting the values into equation 1;
[tex] Average \; speed = \frac {2x}{\frac {5x}{60}} [/tex]
[tex] Average \; speed = \frac {2x*60}{5x} [/tex]
[tex] Average \; speed = \frac {120}{5} [/tex]
Average speed = 24 km/h
A car moving east at a velocity of 16.0 m/s collides with a stationary truck with exactly twice the mass. If the two vehicles lock together, calculate the velocity of their combined mass immediately after collision
Answer:
5.33ms-¹
Explanation:
that is the procedure above
Why potential energy become equal to kinetic energy at height
Answer:
because potentil energy is redy to go but its bound up
And kinetic energy is in motion
Explanation:
The brakes in car A and car B stop working and they need to stop. Car A and car B have the same mass. Car A is traveling at 30 miles per hour, smashes into a big wall, and is brought to rest in a collision that lasts for a fraction of a second. Car B was also traveling at 30 mph but it drives out into a field of grasses and sand and finally comes to rest after a bumpy 20 second ride. Which car gets the larger impulse?
Answer:
Both have equal impulse.
Explanation:
Let the mass of cars be m.
Then the Force acting on each of them for taking them to state of rest:
(Using Newton's second law of motion)
[tex]F_A=\frac{m\times (0-30)}{\Delta t_A}[/tex]
[tex]F_A=-30\frac{m}{\Delta t_A}[/tex] ...................................(1) (negative sign is associated with direction, here we are concerned about the magnitude only)
[tex]F_B=\frac{m\times (0-30)}{\Delta t_B}[/tex]
[tex]F_B=-30\frac{m}{\Delta t_B}[/tex] ...................................(2)
[tex]\because \Delta t_A<\Delta t_B[/tex]
[tex]\therefore F_A>F_B[/tex]
We know that impulse is given as:
[tex]J=F\times \Delta t[/tex] ........................................(3)
So, from eq. (1), (2) & (3)
[tex]J_A=F_A\times \Delta t_A[/tex]
[tex]J_A=-30m[/tex]
&
[tex]J_B=F_B\times\Delta t_A[/tex]
[tex]J_B=-30m[/tex]
Hence both have equal impulse.
6. traction a. friction between a tire and the road.b. pushes a moving object out of a curve and into a straight linec. the ability of a car to hold a straight lined. a road higher in the center than on either edge 7. kinetic energy a.a force that keeps objects moving in a straightb. reduces the effects of inertiac. energy of motiond. a road higher in the center than on either edge 8. force of impact a. a force that keeps objects moving in a straight line.b. a road higher in the center than on either edgec. the force with which a moving vehicle hits another objectd. perception distance, reaction distance, and braking distance
Answer:
6. a. friction between a tire and the road
7. c. energy of motion
8. c. the force with which a moving vehicle hits another object
Explanation:
6. As a car moves along the road, the tires push back against the ground. As tires push back against the ground, the road exerts and opposing force to the motion of the tires. This opposing force is the friction between the tires and the road. This opposing force between the tires and the rad is called traction.
So, the answer is a
7. As an object moves, it has energy. This energy due to its motion is called kinetic energy.
So, the answer is c
8. When a moving vehicle hits another object, it exerts a force on the object. The process of the vehicle hitting the other object is called impact and the force exerted on the object is called the force of impact.
So, the answer is c.
If the mirror reflection coefficients for a laser resonator of length 5 m are 98.5% and 60%, and there are no losses, determine the cavity threshold gain
Answer:
n sei
Explanation:
n seei
Answer:
i relly need help with points it whould help if you make me brainliest
Explanation:
¿Qué diferencia una magnitud fundamental de una derivada?
Answer:
Explanation:
Una magnitud fundamental es aquella que se define por si misma y es independiente de las demás (masa, tiempo, longitud, etc.). magnitud derivada. Una magnitud derivada es aquella que se obtiene mediante expresiones matemáticas a partir de las magnitudes fundamentales (densidad, superficie, velocidad).
A hamster in it's ball starts at rest and accelerates to 3ms1 in 6 seconds.
What was the distance the hamster travelled
Answer:9m
Explanation:
Ball starts from rest . Time taken = 6 seconds. Distance travelled by ball. ∴Distance travelled = 9 m
Hope it helps you
Good luck
a cyclist has a combined mass of 88 kg and a combined weight of 862.4 then accelerates at 1.2m/s after 2 seconds he reaches a of 2.4m/s what is his momentum at this point
Answer:
shushhhgggvvv vgfxgh
Explanation:
gey laahhg
While visiting the beach, you enjoy the warm ocean water, but the sand burns your feet. That night you walk along the beach and notice that the sand is colder than the ocean water. Why?
Group of answer choices
It takes a long time for sand to heat up, but it cools down very quickly. Water takes a short time to heat up and cool down.
Since sand can heat up quickly, it will also cool off quickly. But water takes a long time to heat up and cool down.
Water is naturally colder than sand.
Sand is naturally colder than water.
The answer would be B..
Since sand can heat up quickly, it will also cool off quickly. But water takes a long time to heat up and cool down.
How does your ear work? 6 mark question
Answer:
It collects sound waves and channels them into the ear canal (external auditory meatus), where the sound is amplified. The sound waves then travel toward a flexible, oval membrane at the end of the ear canal called the eardrum, or tympanic membrane. Sound waves cause the eardrum to vibrate.
It collects sound waves and channels them into the ear canal (external auditory meatus), where the sound is amplified. The sound waves then travel toward a flexible, oval membrane at the end of the ear canal called the eardrum, or tympanic membrane. Sound waves cause the eardrum to vibrate. Explanation:
The Outer Ear
The auricle (pinna) is the visible portion of the outer ear. It collects sound waves and channels them into the ear canal (external auditory meatus), where the sound is amplified.
The sound waves then travel toward a flexible, oval membrane at the end of the ear canal called the eardrum, or tympanic membrane. Sound waves cause the eardrum to vibrate.
The Middle Ear
The vibrations from the eardrum set the ossicles into motion. The ossicles are actually tiny bones — the smallest in the human body. The three bones are named after their shapes: the malleus (hammer), incus (anvil) and stapes (stirrup). The ossicles further amplify the sound.
The tiny stapes bone attaches to the oval window that connects the middle ear to the inner ear. The Eustachian tube, which opens into the middle ear, is responsible for equalizing the pressure between the air outside the ear and that within the middle ear.
The Inner Ear
The sound waves enter the inner ear and then into the cochlea, a snail-shaped organ. The cochlea is filled with a fluid that moves in response to the vibrations from the oval window. As the fluid moves, 25,000 nerve endings are set into motion. These nerve endings transform the vibrations into electrical impulses that then travel along the eighth cranial nerve (auditory nerve) to the brain.
The brain then interprets these signals, and this is how we hear.
The inner ear also contains the vestibular organ that is responsible for balance.
What is pulling force? Give any two examples.,
Answer:
Push or Pull Forces - example
When you push against a wall the force that you exert is an example of a push force. When you pull a trolley car the force that you exert is an example of pull force.
which of the following is not an equation of motion:- v=u+at; s=ut+at; v^2-u^2=2as; s=ut+1/2 at^2
Answer:
s=ut+at
its not the equation of motion..
hope it helps stay safe healthy and happy.....The rear wheels of a tractor are very wide. Why?
Answer:
The rear wheels of a tractor are very wide so that the weight of the tractor spread over the greatest surface area possible ,so it doesnot sink into the soil.please as brainliest
Which component of weight is cause for S.H.M of bob simple pendulum
Explanation:
The Simple Pendulum. A simple pendulum is defined to have a point mass, also known as the pendulum bob, which is suspended from a string of length L with negligible mass ((Figure)). Here, the only forces acting on the bob are the force of gravity (i.e., the weight of the bob) and tension from the string.
hope it helps you
which type of image is formed by convex lens on a screen?
Answer:
The type of image formed on a screen by a convex lens is real, enlarged and inverted.
Explanation:
A lens can be defined as a transparent optical instrument that refracts rays of light to produce a real image.
Basically, there are two (2) main types of lens and these includes;
I. Diverging (concave) lens.
II. Converging (convex) lens.
A converging lens refers to a type of lens that typically causes parallel rays of light with respect to its principal axis to come to a focus (converge) and form a real image.
Basically, the type of image formed on a screen by a converging (convex) lens is real, enlarged and inverted because it is usually thick across the middle (causing rays of light to converge) but thin at the lower and upper edges.
A student places a block on a table and hangs one mass from the block. The student lets the block go and observes the block accelerate toward the end of the table where the mass was located. The student then places the block on the table and hangs a second, larger mass from the opposite end of the block. The block accelerates in the opposite direction from the first trial. What does this experiment demonstrate? Answer:
Magnitude of acceleration
Explanation:
We know that acceleration can increase depending in the force applied on an object, any object with a greater mass will apply a greater force. F = M(a).
This Newton's second law establishes a relationship between the summary of the external force and the acceleration of the body, It is demonstrated with the change in the direction and magnitude of the acceleration in the experiment
Newton's second law establishes a relationship between the net force and the acceleration, according to the expression
∑ F = m a
where ∑F is the sum of the external forces, m the mass and the acceleration of the body
In this case we have an initial situation, the block and a baking mass, therefore an acceleration is created towards the hanging mass given by
W₁ = M₁ g
F = ma
M₁ g = m a
a = [tex]\frac{M_1}{m} \ g[/tex]
where W₁ and M₁ are the weight and the masses of the mass of the body hanging under the acceleration of gravity.
In the second case, perhaps you have two masses, one on each side,
∑ F = W₁ -W₂
∑F = (M₁ -M₂) g
let's use Newton's second law
(M₁ -M₂ ) g = m a
a = [tex]\frac{M_1 - M_2}{m} \ g[/tex]
We can see that in the second case the acceleration depends on the difference of the hanging masses. This is a proof of Newton's second law where the effect on acceleration is due to the sum of all external forces and not of each force individually.
In conclusion with the realization of this experiment demostrate the valid true of Newton's second law
Learn more about Newton's second law here: https://brainly.com/question/19860811
what is measurement?
prove that vector addition obeys commutative and associative laws
the order of vector addition doesn't affect the resultant vector and grouping or order of pair doesn't effect the sum.
Beginning at the synapse of a neuron, place the events in neuronal signaling in the correct sequence.1. Ion channels bind the ligand and open.2. Na+ is pumped out of the cell, and the membrane potential is restored.3. Acetylcholinesterase breaks down acetylcholine.4. Na+ enters the postsynaptic cell, and the membrane potential changes.5. Acetylcholine is released into the synapse.6. Na+ ion channels close.A. 3, 4, 6, 1, 5, 2B. 5, 1, 4, 3, 6, 2C. 4, 5, 1, 2, 6, 3D. 1, 2, 3, 4, 5, 6E. 6, 4, 3, 1, 2, 5
Answer:
B. 5, 1, 4, 3, 6, 2
Explanation:
Acetylcholine (ACh) is a molecule that functions as a neurotransmitter and plays diverse roles in brain and muscle function. Ach is released by the presynaptic neurons into the synaptic cleft. The nicotinic acetylcholine receptors are ACh ligand-gated ion channels located at the postsynaptic membrane which admit both sodium (Na+) and potassium (K+) ions. These receptors bind ACh, increasing the permeability of the postsynaptic membrane to Na+ and K+ ions. In consequence, ion channels open and sodium (Na+) ions enter the postsynaptic cell, causing the postsynaptic membrane to depolarize. An enzyme known as acetylcholinesterase breaks down acetylcholine into acetate and choline. If depolarization passes a threshold potential, an action potential is generated in the postsynaptic membrane. The generation of a postsynaptic potential at the excitatory synapse is known as excitatory postsynaptic potential. Once depolarization is complete, Na+ channels close and membrane permeability to Na+ ions declines to the resting levels.
As a girl pushes and object across a wood floor she suddenly comes to an area where the floor has been waxed recently making it slippery . What becomes true if the coefficient of kinetic friction
Answer:
This question is incomplete but the completed question is below
As a girl pushes an object across a wood floor, she suddenly comes to an area where the floor has been waxed recently, making it slippery. What becomes true of the coefficient of kinetic friction? A. The coefficient of kinetic friction increases. B. The coefficient of kinetic friction decreases. C. The coefficient of kinetic friction becomes zero. D. The coefficient of kinetic friction becomes negative.
The correct option is B
Explanation:
Coefficient of kinetic friction can be defined as the frictional force resisted by the motion of an object. From the question, it might take the girl to apply a force equivalent to just half that of the weight of the object to overcome friction to keep the object moving on a wood floor. Once she gets to the waxed area, the frictional force reduces, thereby also reducing the coefficient of kinetic friction further. Thus, she will be able to use less than half of the force (equivalent to less than half of the weight of the object) to push the object.
Thus, the correct option is B.
Elements that typically give up electrons CHECK ALL THAT APPLY
A. are nonmetals
B. have a lower ionization energy
C. include the halogens
D. are metals
Answer:
B. have a lower ionization energy
D. are metals
Explanation:
An atom can be defined as the smallest unit comprising of matter that forms all chemical elements. Thus, atoms are basically the building blocks of matters and as such determines or defines the structure of a chemical element.
Generally, atoms are typically made up of three distinct particles and these are protons, neutrons and electrons.
In Chemistry, electrons can be defined as subatomic particles that are negatively charged and as such has a magnitude of -1.
Valence electrons can be defined as the number of electrons present in the outermost shell of an atom. Valence electrons are used to determine whether an atom or group of elements found in a periodic table can bond with others. Thus, this property is typically used to determine the chemical properties of elements.
Valency can be defined as a measure of the combining power of a chemical element with other atoms to form a molecule or chemical compound.
Typically, valency is measured by the amount of hydrogen atoms that a chemical element can combine with or displace to form a molecule or chemical compound.
Ionization energy can be defined as the minimum energy required to remove or detach an electron from a neutral atom in a gaseous state.
Generally, the ionization energy of chemical elements tend to increase from left to right across a period on the periodic table. This increase is due to the fact that the atomic radius of chemical elements generally decreases across the periodic table, typically from alkali metals (group one elements such as hydrogen, lithium and sodium) to noble gases (group eight elements such as argon, helium and neon) i.e from left to the right of the periodic table. Also, the atomic radius of a chemical element increases down each group of the periodic table, typically from top to bottom (column).
This ultimately implies that, atoms with relatively large atomic radii tend to have a low electron affinity and a low ionization energy.
In conclusion, chemical elements that typically give up electrons are metals because their outermost shell contains excess electrons and have a lower ionization energy.
Define couple and give 2 examples
Answer:
Two equal and opposite parallel forces not acting along the same line, form a couple. A couple is always needed to produce the rotation.
For example, turning a key in a lock and turning a steering wheel.
Your parallel capacitors are 15 μf and 20 μf. The series capacitors are 10 μf and 12 μf. This circuit is connected to a 14 v battery, also determine the potential energy and the voltage across each capacitor
Answer:
a. i. 6.608 V ii. 5.507 V iii. 1.89 V iv. 1.89 V
b. i. 0.22 mJ ii. 0.182 mJ iii. 0.027 mJ iv. 0.036 mJ
Explanation:
a. The voltage across each capacitor
Since the 15 μf and 20 μf capacitors are in parallel, their total capacitance is C = 15 μf + 20 μf = 35 μf.
Also, since C is in series with the 10 μf and 12 μf which are in series, their total capacitance, C' is gotten from 1/C' = 1/10 μf + 1/12 μf + 1/35 μf
1/C' = (12 + 42 + 35)/420 /μf
1/C' = 89/420 /μf
C' = 420/89 μf
C' = 4.72 μf
The total charge in the circuit' is thus Q = C'V where V = voltage = 14 V
So, Q = C'V = 4.72 μf × 14 V = 66.08 μC
Since the 10 μf and 12 μf are in series, Q is the charge flowing through them.
Since Q = CV and V = Q/C
i. The voltage across the 10 capacitor is
V = 66.08 μC/10 μF = 6.608 V
ii. The voltage across the 12 capacitor is
V = 66.08 μC/12 μF = 5.507 V
The voltage across the 15 μF and 20 μF capacitors.
Since the capacitors are in parallel, the voltage across them is the voltage across their combined capacitance, C
So, V = Q/C = 66.08 μC/35 μF = 1.89 V
iii. The voltage across the 15 μF capacitor is 1.89 V
iv. The voltage across the 20 μF capacitor is 1.89 V
b. The potential energy of each capacitor
i. The potential energy of the 10 μF capacitor
E = 1/2CV² where C = Capacitance = 10 μF = 10 × 10⁻⁶ F and V = voltage across capacitor = 6.608 V
E = 1/2CV²
E = 1/2 × 10 × 10⁻⁶ F(6.608 V)²
E = 5 × 10⁻⁶ F(43.666) V²
E = 218.33 × 10⁻⁶ J
E = 0.21833 × 10⁻³ J
E = 0.21833 mJ
E ≅ 0.22 mJ
ii. The potential energy of the 12 μF capacitor
E = 1/2CV² where C = Capacitance = 12 μF = 12 × 10⁻⁶ F and V = voltage across capacitor = 5.507 V
E = 1/2CV²
E = 1/2 × 12 × 10⁻⁶ F(5.507 V)²
E = 6 × 10⁻⁶ F(30.327) V²
E = 181.96 × 10⁻⁶ J
E = 0.18196 × 10⁻³ J
E = 0.18196 mJ
E ≅ 0.182 mJ
iii. The potential energy of the 15 μF capacitor
E = 1/2CV² where C = Capacitance = 15 μF = 15 × 10⁻⁶ F and V = voltage across capacitor = 1.89 V
E = 1/2CV²
E = 1/2 × 15 × 10⁻⁶ F(1.89 V)²
E = 7.5 × 10⁻⁶ F(3.5721) V²
E = 26.79 × 10⁻⁶ J
E = 0.02679 × 10⁻³ J
E = 0.02679 mJ
E ≅ 0.027 mJ
iv. The potential energy of the 15 μF capacitor
E = 1/2CV² where C = Capacitance = 20 μF = 15 × 10⁻⁶ F and V = voltage across capacitor = 1.89 V
E = 1/2CV²
E = 1/2 × 20 × 10⁻⁶ F(1.89 V)²
E = 10 × 10⁻⁶ F(3.5721) V²
E = 35.721 × 10⁻⁶ J
E = 0.035721 × 10⁻³ J
E = 0.035721 mJ
E ≅ 0.036 mJ
Why does time have a direction? Please give your ideas I want to see them. Brainliest f0r most effort.:)
Answer:
it's a rule like water !!!!
Explanation:
Most importantly, time appears to run forward always never backwards. in other words there's perceived arrow of time and there's thermodynamic arrow of time, and they always point in a forward direction
for every system there are more states that seem chaotic then states that seem ordered.
the arrow of time seems to have something to do with that tendency. but to get from one instance to another where things get more entropy, we already need some kind of time, gotta admit that.
some (physicists) believe that time is an illusion, that the whole universe is already set in stone, like a block (the idea is therefore called block universe). from the perspective of a godlike outside observer the universe would be like a book, or a 4D movie. the characters might feel a movement of things in a direction, but rewinding it wouldn't feel different in any instance because the order in wich things happen is already written.
a different idea is that there are infinite many different futures and the further they are away, the less we can know for sure about them in a physical way. and this might also be work for the past, so that different parts could lead to one present.
when macroscopic information is deleted, it might not be reversible, so the past gets ultimately blurry. one example for deletion of macroscopic information this is the Library of Alexandria wich burned down.
all the quantum information is still conserved, but the order of things (like letters on pages) is lost and could have been in different configurations before. we can't ultimately not even see the past, as much as we would try.
personally the idea that the past is written in stone but the future is in flux doesn't make any sense for me. because than I could have free will now, but not from the perspective 10 days later.
the present would be a very special thing than, the stage where the universe likes to play.
maybe we can get a grasp on time if we look at it like rules for a game, like a cardboard game.
To get from one configuration to the next ,we must follow rules. like throwing dice and moving in monopoly.
gravity would be a simple real world example for such a rule, a natural law.
But no one would have a firm clue where this rules came from.
TLDR: I don't know and neither does anyone else for sure, not even top notch scientists.
the hardest questions are easy to formulate, but maybe even impossible for us to answer in a satisfying way. I hope we will understand those hard questions better one day, and maybe even get answers.
What is the form of the main energy output from the reactor?
Explanation:
A nuclear reactor produces and controls the release of energy from splitting the atoms of certain elements. In a nuclear power reactor, the energy released is used as heat to make steam to generate electricity.
What is the dependent variable in this
experiment?
DONE
Biologists designed an experiment to test
the effect of compost on the development
of root crops. They tested several different
crops, including carrots, potatoes, beets,
and onions. They grew most of the plants
in the greenhouse, but due to space issues,
they had to grow some outdoors. They gave
all the plants the same amount of compost.
They obtained the compost from a local
farmer and from the local hardware store.
They ran out of the farmer's compost, so
some of the plants received that compost
when the seeds were planted and other
plants got hardware store compost after
the plants had already started growing.
What is the independent variable in this
experiment?
DONE
Answer:
"the plants had already started growing."
Explanation:
I think this is the answer because the definition of a dependent variable is the variable that is being affected by the change. Since the plants had already started growing BECAUSE of "They ran out of the farmer's compost, so
some of the plants received that compost
when the seeds were planted and other
plants got hardware store compost after
the plants had already started growing."
Sorry if I am wrong, I am just a 4th grader, pls don't hate on me, I am just trying to help :)
Answer:
It's compost
Explanation:
In case you needed the dependent variable, its the amount of plant growth
A weightlifter lifts a 500 N barbell with no acceleration, 1.25 meters. How much work did she do in lifting the weights?(step by step)
Answer:
–625 J
Explanation:
So, we got this formula for the work
W=mgd(Cosθ)
but remember when it's liftin somethin, its work gon be against the work of gravity, so
Cos180°= –1
W=500×1.25×(–1)
W= –625 J
URGENT A student runs at 4.5 m/s [27° S of W] for 3.0 minutes and then he turns and runs at 3.5 m/s [35° S of E] for 4.1 minutes. a. What was his average speed? b. What was his displacement? PLEASE SHOW ALL WORK
Answer:
Explanation:
As far as the displacement goes, we have 2 displacement vectors. If we didn't have the angles to deal with, this would be a much simpler process, but then that wouldn't be any fun at all, would it? I'll deal with the average speed first, then the displacement, which is a vector addition problem.
The average speed is found by adding together the distances the student traveled and then dividing this sum by the total time he spent traveling. If we are told that the student runs at 4.5 m/s for 3.0 minutes, we can use this to find out the distance he ran during that time interval. However, the units are not the same. We will find the distance the student traveled by convering the time to seconds.
3.0 minutes = 180 seconds, and
4.1 minutes = 246 seconds.
That means that the distance he ran in 180 seconds is found by multiplying this time be the speed at which he ran:
4.5 m/s(180 s) = 810 m and
3.5 m/s(246 s) = 860 m (rounded to follow the rules of sig dig).
This makes the speed equation look like this:
[tex]s=\frac{810+861}{180+246}=\frac{1671}{426}=3.9\frac{m}{s}[/tex] That's the average speed, which is NOT at all the same as the displacement. Displacement is where he ended up in reference to where he started. The angles play a huge part in this math (that is very involved, to say the least). We begin by restating the displacement of each "leg" of this journey.
The first leg took him 810 m at 207 degrees and
the second leg took him 860 m at 325 degrees
To find the x and y components of these 2 legs, or parts, we have to use the cos and sin formulas. We will call the first leg A and the second leg B. First the x components of both A and B:
[tex]A_x=810cos207[/tex] and
[tex]A_x=-720[/tex]
[tex]B_x=860cos325[/tex] and
[tex]B_x=704[/tex] and we add these to get the x-component of the resultant vector, C:
-720
+ 704
-10 (rounded, as needed, to the tens place).
Now for the y-components of the resultant vector:
[tex]A_y=810sin207[/tex] and
[tex]A_y=-370[/tex]
[tex]B_y=860sin325[/tex] and
[tex]B_y=-490[/tex] and we add these to get the y-component of the resultant vector, C:
-370
+ -490
-860
Since the x component is negative and so is the y, we are in QIII, so when we finally find our angle, we will have to add 180 to it.
For the magnitude of the displacement vector, in m:
[tex]C_{mag}=\sqrt{(-10)^2+(-860)^2}[/tex] which gives us
[tex]C_{mag}=860m[/tex]
Now, because displacement is vector, we also need the angle. We find that is the formula
[tex]\theta=tan^{-1}(\frac{C_y}{C_x})[/tex] and filling in:
[tex]\theta=tan^{-1}(\frac{-860}{-10})=90[/tex] (rounded correctly), and then we add 180 to give us a final direction of 270 degrees.
So the final displacement of the student is 860 m at 270 degrees