Answer:
It was proposed by Isaac Newton
Explanation:
The law of universal attraction of expression
F = [tex]G \ \frac{m_1m_2}{ r^2}[/tex]G m1m2 / r ^ 2
where G is a constant, m₁ and m₂ are the masses of the bodies and r the distance between them.
It was proposed by Isaac Newton
With this law Newton explained that the force that pulls the moon towards the earth is the same as that which attracts an apple towards the earth
Eli states that sodium phosphate is a mixture because it is composed of both sodium ions and phosphate ions.
Which is the best analysis of Eli’s statement?
The question is incomplete, the complete question is;
Eli states that sodium phosphate is a mixture because it is composed of both sodium ions and phosphate ions. Which is the best analysis of Eli’s statement? It is correct because each ion is a pure substance, so sodium phosphate is made up of two pure substances. It is correct because the composition of sodium phosphate changes depending on the sample. It is incorrect because sodium phosphate is a compound that has a single composition. It is incorrect because the two types of ions in sodium phosphate cannot be seen.
Answer:
It is incorrect because sodium phosphate is a compound that has a single composition
Explanation:
A compound is a neutral substance made up of two or more atoms which are chemically combined together.
Ionic substances are made up of ions. These ions are not separate entities, they are part of the compound.
Hence, Eli's statement is incorrect because sodium phosphate is a compound that has a single composition.
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.
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.
Define ELASTIC LIMIT, YIELD POINT AND ULTIMATE TENSILE STRENGTH?
[tex] \green{\huge{\red{\boxed{\green{\mathfrak{QUESTION}}}}}} [/tex]
ELASTIC LIMIT, YIELD POINT AND ULTIMATE TENSILE STRENGTH.
[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{TOPIC}}}}}}} [/tex]
Mechanical Properties Of Solid.
[tex] \huge\green{\boxed{\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}}}[/tex]
[tex] \bold{ \green{PART \: \: (1):-}} \\ \bold \green {{ ELASTIC \: \: LIMIT}}[/tex]
It is also called yield point
In this limit, energy provided to the material to cause deformation when removed then the material returns to its own shape and size.
In this limit each body shows elastic nature
[tex] \bold{ \red{PART \: \: (2):-}} \\ \bold \red {{YIELD \: \: STRENGTH}}[/tex]
It is the fix amount of the energy which causes fixed permanent set of deformation.
In this body shows plastic deformation.
The level of stress that corresponds to the yield point is referred to as the yield strength of the material.
[tex]\bold{ \purple{PART \: \: (3):- \:ULTIMATE }} \\ \bold \purple {{TENSILE \: \: STRENGTH}}[/tex]
It is the amount of the stress which causes permanent set of deformation after the yield point.
Body show perfect plastic deformation.
This shows a permanent set of deformation.
[tex] \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star[/tex]
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.
¿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 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
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.
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 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
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.
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
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
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
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.
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
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:
a sprinter runs 100m in12.5seconds calculate the speed
Answer:
8m in 1 second
480m = 1 hour
11,520m in one day
Explanation:
Hope this is helpful
what is measurement?
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.
Margy is trying to improve her cardio endurance by performing an exercise in which she alternates walking and running 100.0 m each. If Margy is walking at 1.4 m/s and accelerates at 0.20 m/s2 during
Complete question is;
Margy is trying to improve her cardio endurance by performing an exercise in which she alternates walking and running 100.0 m each. If Margy is walking at 1.4 m/s and accelerates at 0.20 m/s² during one of the running portions, what is her final velocity at the end of the 100.0 m? Round your answer to the nearest tenth.
Answer:
6.5 m/s
Explanation:
We are told that she is walking at 1.4 m/s and accelerates at 0.20 m/s².
Thus;
Initial velocity; u = 1.4 m/s
Acceleration; a = 0.2 m/s²
Distance; s = 100 m
From Newton's equation of motion, we know that;
v² = u² + 2as
Where v is final velocity.
Thus;
v² = 1.4² + 2(0.2 × 100)
v² = 41.96
v = √41.96
v ≈ 6.5 m/s
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
explain why it is important that the Earths atmosphere absorbs gramma rays emitted by the sun
Answer:
Gamma rays have so much energy they could harm people on Earth. People are protected from gamma rays by Earth's atmosphere. The atmosphere absorbs gamma rays, preventing them from affecting life on Earth. Because gamma rays cannot penetrate Earth's atmosphere, scientists use satellites in space to study them.
Answer:
Explanation:
because gamma rays have so much energy they could harm people on earth
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.
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.
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
Please help it's for a test that is due right now.
A car of mass 1000kg is traveling 30m/s
a) What is the kinetic energy?
b) How high will it have to travel up a hill to have the same potential as kinetic energy as this speed? Remember Ep-Ek
Answer:
a. 15,000J
b. .76m
Explanation:
KE = (1/2)m*v²
KE = .5*1000kg*30m/s
KE = 15000J
PE = m*g*h
7500J = 1000kg*9.81m/s²*h
7500J = 9810*h
h = .76m
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.
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
