Hi there!
(A)
A grinding wheel is the same as a disk, having moment of inertia of:
[tex]I = \frac{1}{2}MR^2[/tex]
Plug in the given mass and radius (REMEMBER TO CONVERT) to find the moment of inertia:
[tex]I = \frac{1}{2}(0.380)(0.085)^2 = 0.00137 kgm^2[/tex]
(B)
We can use the rotational equivalent of Newton's Second Law to calculate the needed torque:
Στ = Iα = τ₁ - τ₂
Begin by solving for the angular acceleration. Convert rpm to rad/sec:
[tex]\frac{1750r}{min} * \frac{1 min}{60 s} * \frac{2\pi rad}{1 r} = 183.26 rad/sec[/tex]
Now, we can use the following equation:
ωf = wi + αt (wi = 0 rad/sec, from rest)
183.26/5 = α = 36.65 rad/sec²
τ = Iα = 0.0503 Nm
Since there is a counter-acting torque on the system, we must begin by finding that acceleration:
[tex]\frac{1500r}{min} * \frac{1 min}{60 s} * \frac{2\pi rad}{1 r} = 157.08 rad/sec[/tex]
ωf = wi + αt
-157.08/55 = α = -2.856 rad/sec²
τ₂ = Iα = 0.0039 Nm
Now, calculate the appropriate torque using the above equation:
[tex]\Sigma\tau = \tau_1 - \tau_2[/tex]
[tex]\Sigma\tau + \tau_2 = \tau_1[/tex]
[tex]0.0503 + 0.0039 = \large\boxed{0.054 Nm}[/tex]
What diameter telescope is needed to resolve the separation between an Earth-like planet and its star at 550 nm if the linear separation between them is 1 AU and the star system is 3 pc from Earth
The Rayleigh criterion allows finding the result for the diameter of the telescope that allows solving the separation of the star and the planet is:
The diameter of the telescope is D = 0.415 m
The Rayleigh criterion is used to find the separation of two points, it is based on the fact that the diffraction maximuum pattern of the first object coincides with the first minimum of the second object.
By entering in the diffraction ratio for slits you will find.
sin θ = [tex]\frac{\lambda}{a}[/tex]
In general in diffraction experiments the angles are very small,
[tex]tan \theta = \frac{y}{x} = \frac{sin \theta}{cos \theta} \\sin \theta = \frac{y}{x}[/tex]
For the case of circular apertures, when solving in polar coordinates, a constant appears.
[tex]\frac{y}{x} = 1.22 \frac{\lambda}{D}[/tex]
[tex]D = 1.22 \frac{\lambda \ x}{y}[/tex]
Where λ is the wavelength of light and D is the diameter of the aperture.
They indicate that the separation between the star and the planet is 1 AU and the distance from the system to the Earth is 3 parce.
Let's reduce the parce to astronomical units
x = 3 pc ( [tex]\frac{206264 AU}{1 pc}[/tex] )
x = 6.18 10⁵ AU
Let's calculate
D = [tex]D = 1.22 \ \frac{550 \ 10^{-9 } \ 6.18 \ 10^5 }{1}[/tex]
D = 0.415 m
In conclusion, using the Rayleigh criterion we can find the result for the diameter of the telescope that allows solving the separation of the star and the planet is:
The diameter of the telescope is D = 0.415 m
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A pumpkin is launched in the air and travels at a horizontal velocity of 25 meters per second for 5 seconds. How far does it travel horizontally?
Answer:
30.3 meters, 172 degrees
Explanation:
To insure the most accurate solution, this problem is best solved using a calculator and trigonometric principles. The first step is to determine the sum of all the horizontal (east-west) displacements and the sum of all the vertical (north-south) displacements.
Horizontal: 2.0 meters, West + 31.0 meters, West + 3.0 meters, East = 30.0 meters, West
Vertical: 12.0 meters, North + 8.0 meters, South = 4.0 meters, North
The series of five displacements is equivalent to two displacements of 30 meters, West and 4 meters, North. The resultant of these two displacements can be found using the Pythagorean theorem (for the magnitude) and the tangent function (for the direction). A non-scaled sketch is useful for visualizing the situation.
Applying the Pythagorean theorem leads to the magnitude of the resultant (R).
R2 = (30.0 m)2 + (4.0 m)2 = 916 m2
R = Sqrt(916 m2)
R = 30.3 meters
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (4.0 m) / (30.0 m)
tangent(theta) = 0.1333
theta = invtan(0.1333)
theta = 7.59 degrees
This angle theta is the angle between west and the resultant. Directions of vectors are expressed as the counterclockwise angle of rotation relative to east. So the direction is 7.59 degrees short of 180 degrees. That is, the direction is ~172 degrees.
A 0.015 kg marble sliding to the right at 0.225 m/s on a frictionless surface makes an elastic head-on collision with a 0.015 kg marble moving to the left at 0.180 m/s. After the collision, the first marble moves to the left at 0.180 m/s. Find the velocity of the second marble after the collision.
Explanation:
[tex]if \: the \: masses \: of \: the \:two \: marbles\: equal \\ then \: each \: velocity \: sharing \: with \: other \: velocity[/tex]
What are some physical factors we deal with for sleeping?
Answer:
we deal our body movement during sleeping
In an oscillating LC circuit, when 86.6% of the total energy is stored in the inductor's magnetic field, (a) what multiple of the maximum charge is on the capacitor and (b) what multiple of the maximum current is in the inductor
We have that for the Question "(a) what multiple of the maximum charge is on the capacitor and (b) what multiple of the maximum current is in the inductor"
Answer:
a) maximum charge = [tex]0.366Q_{max[/tex]b) maximum current = [tex]0.931I_{max}[/tex]
From the question we are told
In an oscillating LC circuit, when 86.6% of the total energy is stored in the inductor's magnetic field
A) When 86.6\% energy is stored in inductor
[tex]\%[/tex]of energy stored in electric field = [tex]1 - 0.866 = 13.4\%[/tex]
[tex]\frac{V_E}{V} = \frac{\frac{q^2}{2c}}{\frac{Q^2}{2c}} = 0.134\\\\\frac{q}{Q} = \sqrt0.134\\\\\frac{q}{Q} = 0.366\\\\q = 0.366Q_{max[/tex]
B)
[tex]\frac{V_B}{V} = \frac{\frac{Li^2}{2}}{\frac{LI^2}{2}} = 0.866\\\\\frac{i}{I} = \sqrt0.866\\\\\frac{i}{I} = 0.931\\\\i = 0.931I_{max[/tex]
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Three point charges are placed on the y-axis: a chargeqaty=a,a charge-2qat the origin, and a chargeqaty= -a.Such an arrangement is called an electricquadrupole.(a) Find the magnitude and direction of the electric field at points on thepositive x-axis. (b) Use the binomial expansion to find an approximate expression for the electric field valid for x >> a.Contrast this behavior to that of the electric field of a point charge and that of the electric field of a dipole.
what were your preparetion before going the different physical fitness test?
Answer:
Avoid heavy strenuous exercise for the 24 hours prior to testing. Do not exercise at all on the day of testing to ensure you are well rested. Wear appropriate clothing for the conditions (e.g. shorts/track pants and t-shirt/singlet/sports top) and non-slip athletic footwear with laces securely fastened
HELP ASAP!!!!! Choose all the answers that apply. Technology A)influences science
B)helps scientists observe fast phenomena
C)is the same as science
D) influences history
E)helps scientists observe slow phenomena
A 500 kg cart is rolling to the right at 1.3 m/s. a 60 kg man is standing on the right end of the cart. what is the speed of the cart if tha man suddenly starts running to the left with a speed 10.0 m/s relative to the cart
Answer:
P1 = 1.3 (500 + 60) = 728 kg-m total momentum to right at start
P2 = (v2 - 10) 60 + 500 v2
total momentum after running at -10 with respect to cart = 728 where v2 is the new speed of the cart
728 = 560 v2 - 600
v2 = 1328 / 560 = 2.37 m/s new speed of cart
Check:
After: p2 for cart = 500 * 2.37 = 1186
p1 for man = (2.37 - 10) * 60 = -458
P2 = p1 + p2 = 728 total momentum unchanged
A wooden barrel full of water has a flat circular top of radius 25.0 cm with a small hole in it. A tube of height 8.00 m and inner radius 0.582 cm is suspended above the barrel with its lower end inserted snugly in the hole. Water is poured into the upper end of the tube until it is full. The density of water is 1.00 × 103 kg/m3.
What is the force with which the water in the barrel pushes up on the top of the barrel?
Answer:
that is all i know
Explanation:
radius= 25.0cm
height= 8m
inner radius= 0.582cm
density= 1.00 × 103kgm³f= m× aTwo ends of a steel wire of length 8m and 2mm radius are fixed to two rigid supports. Calculate the increase in tension when the temperature falls by 10°C. Given linear expansivity of steels = 12x10^_6 per kelvin and Young's modules for steel =2x10^11 n/m^2
The increase in tension on the steel wire is 8,484.75 N.
The given parameters;
original length of the wire, l = 8 mradius of the wire, r = 2 mmThe area of the steel wire is calculated as follows;
[tex]A = \pi r^2\\\\A = \pi \times (2\times 10^{-3})^2\\\\A = 1.257 \times 10^{-5} \ m^2[/tex]
The extension of the steel wire is calculated as follows;
[tex]\Delta l = \alpha \times l\times \Delta T\\\\\Delta l = (12\times 10^{-6}) \times (8) \times (10 + 273)\\\\\Delta l = 0.027 \ m[/tex]
The increase in tension on the steel wire is calculated as follows;
[tex]E = \frac{stress}{strain } = \frac{\ F/A}{\Delta l/l} \\\\E = \frac{F\times l}{A \times \Delta l} \\\\F = \frac{E\times A \times \Delta l }{l} \\\\F = \frac{(2\times 10^{11}) \times (1.257\times 10^{-5})\times 0.027}{8} \\\\F = 8,484.75 \ N[/tex]
Thus, the increase in tension on the steel wire is 8,484.75 N.
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5) You pull a 10.0 kg wagon along a flat road. You exert a force of 80.0 N at an angle of 30.0 degrees above the horizontal while you move the wagon 10.0 m forward. The coefficient of friction between the wagon and road is 0.500. Calculate the work down by you and the work done by friction.
Consult the attached free body diagram. The only forces doing work on the wagon are the frictional force opposing the wagon's motion and the horizontal component of the applied force.
By Newton's second law, the net vertical force is
• ∑ F [v] = n + (80.0 N) sin(30.0°) - mg = 0
where a is the acceleration of the wagon.
Solve for n (the magnitude of the normal force) :
n = (10.0 kg) g - (80.0 N) sin(30.0°) = 58.0 N
Then
f = 0.500 (58.0 N) = 29.0 N
Meanwhile, the horizontal component of the applied force has magnitude
(80.0 N) cos(30.0°) ≈ 69.3 N
Now calculate the work done by either force.
• friction: -(29.0 N) (10.0 m) = -290. J
• pull: (69.3 N) (10.0 m) = 693 J
what do i do for #17
Answer:
whats the question...............
Explanation:
A person is pushing a box with 5 N to the right while another person pushes with 10 N to the left, what is the net force on the box?
Answer:
Fnet = 5 Newton
Explanation:
Fnet = 10 N - 5 N
Fnet = 5 N
Check all true statements about nonmetals. Group of answer choices
All nonmetals are gaseous at room temperature.
Nonmetals have low melting and boiling points. ✅
Nonmetals are brittle and have a relatively low density. ✅
Nonmetals are good at thermal and electrical conduction.
Using the colored periodic table below, match the group or area to its color.
alkali metals red alkaline ✅
earth metals orange ✅
transition metals white ✅
halogens purple ✅
Nobel gasses teal✅
How many of each subatomic particle are in a neutral atom of Potassium-39? What is its mass number? Potassium is in group 1 and has the symbol "K".
protons 19 ✅
neutrons 20 ✅
electrons 19 ✅
mass number 39✅
Match the ion with its charge.
11 protons, 12 neutrons, 10 electrons = +1 ✅
Groups 17, period 2 = -1 ✅
31 protons, 39 neutrons, 28 electrons = +3✅
Group 2, period 5 = +2
Which best describes a metal such as Silver (Ag)?
Answer: Lustrous, malleable, and forms cations.
Determine if the "quoted" word(s) makes each statement True or False.
Elements that share the most characteristics are found on the periodic table in the same "horizontal period". False ✅
If matter has a higher temperature, that means there will be "more" molecular motion. True✅
If you put a balloon in a freezer, its volume would "increase". False ✅
If you put the balloon into a chamber where there is half the pressure, its volume will "double". True ✅
If you cool down a propane tank, there will be "less" pressure in it. True ✅
The average atomic mass of Aluminum (Al) is "16.00 amu".
False✅
Oxygen's atomic number is "8" therefore it has "8" protons in its nucleus. True✅
An "electron" has the same mass as a neutron. False✅
The nucleus contains "protons and neutrons", virtually all the mass of an atom.✅
Metals are found towards the left hand side of the periodic table while Nonmetals are found towards the right hand side of the periodic table.
Non metals are found towards the right hand side of the periodic table. They are not all gaseous at room temperature some nonmetals such as iodine are solid at room temperature.
Nonmetals usually have low melting and boiling points, are brittle, have relatively low density and are not good at thermal and electrical conduction.
Potassium - 39 contains 19 protons, 20 neutrons and 19 electrons. Recall that the number of protons and electrons are equal in a neutral atom.
The following is an accurate matching of the ions;
11 protons, 12 neutrons, 10 electrons = +1 - Na^+
31 protons, 39 neutrons, 28 electrons = +3 - Ga^2+
Group 2, period 5 = +2 - Sr^2+
Silver is a lustrous metal.
Elements that share the most characteristics are found on the periodic table in the same "horizontal period". FalseIf matter has a higher temperature, that means there will be "more" molecular motion. TrueIf you cool down a propane tank, there will be "less" pressure in it. TrueIf you put a balloon in a freezer, its volume would "increase". FalseIf you put the balloon into a chamber where there is half the pressure, its volume will "double". TrueThe average atomic mass of Aluminum (Al) is "16.00 amu". FalseOxygen's atomic number is "8" therefore it has "8" protons in its nucleus. TrueAn "electron" has the same mass as a neutron. FalseThe nucleus contains "protons and neutrons", virtually all the mass of an atom - True
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Answer:
If your answers are the green check marks all of them are correct
Explanation: I took the test
of the following which is the largest body?
a. the moon
b. Pluto
c. Mercury
d. Ganymede
Answer:
Ganymede is the largest body
Explanation:
it is the satellite of jupiter
A less than youthful 82.6 kg physics professor decides to run the 26.2 mile (42.195 km) Los Angeles Marathon. During his months of training, he realizes that one important component in running a successful marathon is carbo-loading, the consumption of a sufficient quantity of carbohydrates prior to the race that the body can store as glycogen to burn during the race. The typical energy requirement for runners is 1 kcal/km per kilogram of body weight, and each mole of oxygen intake allows for the release of 120 kcal of energy by oxidizing (burning) glycogen.
(a) If the professor finishes the marathon in 4:45:00 h, what is the professor's oxygen intake rate, in liters per minute, during the race if he metabolizes all of the carbo-loaded glycogen during the race and the ambient temperature is 21.5°C? 2.28 Read the problem statement again carefully. Is the air at standard temperature and pressure during the marathon? How would this affect the volume of 1 mol of oxygen? L/min
(b) The human body has an efficiency of 25.0%. Only 25.0% of the energy released from oxidizing glycogen is used as macroscopic mechanical energy, and the remaining 75.0% is used for body processes such as pumping blood and respiration, and then leaves the body through the skin via radiation, evaporative cooling, and other processes. What is the average mechanical power (in W) generated by the professor during the run? 197.561 What is the total energy required by the professor during the run? How efficient is the human body, and how long did the race last? W
(c) What is the change in entropy (in J/K) of the professor's body if his core temperature has risen to 38.3°C during the run and his skin temperature is at 36.0°C during the marathon? J/K
(d) What is the change of the entropy (in J/K) of the air surrounding the professor during the race if the ambient temperature remains constant at 21.5°C? J/K
A 5 kg bowling ball travelling at 2 m/s hits a motionless 10 kg bowling ball. If the smaller ball bounces back at a speed of -1 m/s, what will be the speed of larger ball after the collision? Hint: Use the conservation of momentum equation to solve this problem.
Answer:
1.5 m/s
Explanation:
Conservation of momentum means the momentum of the system before the collision is the same as after.
The before, after momentum of each ball is ...
5 kg ball: (5 kg)(2 m/s), (5 kg)(-1 m/s)
10 kg ball: (10 kg)(0 m/s), (10 kg)(v)
The sum of the "before" products is the same as the sum of the "after" products:
(5 kg)(2 m/s) +0 = (5 kg)(-1 m/s) +(10 kg)v
(10 +5) kg·m/s = (10 kg)·v . . . . . add (5 kg)(1 m/s) to both sides
v = (15 kg·m/s)/(10 kg) = 1.5 m/s
The speed of the larger ball will be 1.5 m/s. Its direction of motion will be the opposite of that of the 5 kg ball after the collision.
An airplane accelerates from a speed of 33 m/s at the constant rate of 3.0 m/s2 over a distance of 500 m. What the final velocity?
Answer:
Explanation:
v² = u² + 2as
v² = 33² + 2(3.0)(500)
v² = 4089
v = 63.9452...
v = 64 m/s
If a = 8i + j - 2k and b = 5i - 3j + k show that a) a x b = -5i - 18j - 29k b) b X a = 50 + 18j +29k
Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
Answer:
Explanation:
If a = 8i + j - 2k and b = 5i - 3j + k show that a) a x b = -5i - 18j - 29k b) b X a = 50 + 18j +29k
I will mark brainlist
A wave is disturbance that transfers energy and matter.
true
false
Answer:
False
Explanation:
A wave is a disturbance that transfers energy from one place to another without transferring matter.
Answer:
I'm pretty sure it true sorry if I'm wrong
Una turbina de vapor
recibe vapor con un flujo másico de 30 kg/s a 6205 kPa, 811 K, con una velocidad a la
entrara de 10 m/s. El vapor a la entrada tiene una energía interna específica de 3150.3
kJ/kg y un volumen específico de 0.05789 m3
/kg. El vapor sale de la turbina a 9.859 kPa,
318.8 K. El vapor sale a 200 m/s con una energía interna específica de 2211.8 kJ/kg y
un volumen específico de 13.36 m3
/kg. Encuentre la potencia producida por la turbina
si ésta pierde calor a una tasa de 30 kW.
Este problema está describiendo una turbina de vapor a la que entra vapor a 30 kg/s, 6.205 kPa y 811 K con una velocidad de 10 m/s y sale a 9.859 kPa, 318.8 K y con una velocidad de 200 m/s. Adicionalmente, tanto el volumen específico como la energía interna son dados para ambas corrientes.
Con lo anterior, resulta posible escribir un balance de energía para esta turbina, despreciando todo efecto por energía potencial ya que no hay diferencia significativa entre la altura de la entrada (1) y la salida (2), pues están practicamente al mismo nivel:
[tex]mh_1+\frac{1}{2} mv^2_1=mh_2+\frac{1}{2} mv^2_2+Q_2+W_2[/tex]
Aquí vemos que la incógnita es [tex]W_2[/tex] como la potencia que produce la turbina. Ahora, el primer cáculo a realizar es el de las entalpías de las corrientes de entrada y salida, dada la energía interna, presión y volumen específico:
[tex]h_1=3150.3\frac{kJ}{kg}+6205kPa*0.05789\frac{m^3}{kg} =3509.51\frac{kJ}{kg}\\\\h_2=2211.8\frac{kJ}{kg}+9.859kPa*13.36\frac{m^3}{kg} =2342.72\frac{kJ}{kg}[/tex]
Ahora, podemos reacomodar el balance de energía con el fin de resolver [tex]W_2[/tex]:
[tex]W_2=m(h_1-h_2)+\frac{1}{2} m(v^2_1-v^2_2)-Q_2[/tex]
Finalmente, reemplazamos los valores para obtener:
[tex]W_2=10\frac{kg}{s} (3509.51-2342.72)\frac{kJ}{kg} +\frac{1}{2} *10\frac{kg}{s} [(10\frac{m}{s}) ^2-(200\frac{m}{s} )^2]*\frac{1kJ}{1000J} -30\frac{kJ}{s}\\\\W_2=11438.4 kJ/s=11438.4kW[/tex]
Es de precisar que la energía cinética como 1/2 m*v² resulta en Joules, por lo que hay que convertir a kilojoules para tener unidades consistentes de kilowatts al final.
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https://brainly.com/question/21902769https://brainly.com/question/24322350please help meee please please
Answer:
I think it's c but don't know for sure
Which is NOT a function of the
cell wall?
A. Protects cell from bursting
B. Provides support for plant cells
C. Protects cell from harsh internal
environments
D. Absorbs sunlight to give energy to the cell
Answer:
The answer is D
Explanation:
The chloroplast absorbs sunlight for energy not the cell wall
The octopus’s tentacle keeps _ right after it is bitten off ? a. Moving b. Breathing c. Growing
Answer:
The answer is A
Explanation:
The octopus’s tentacle keeps moving right after it is bitten off
A motorcycle moves according to the velocity-time graph
shown in Figure 3.28. Find the average acceleration of
the motorcycle during each of the following segments of
the motion: (a) A, (b) B, and (c) C.
Answer:
a) 1 m/s²
b) -1 m/s²
c) 0 m/s² (constant speed, not accelerating)
Explanation:
A
delta speed = 10 - 0
delta time = 10 - 0
delta speed / delta time = 10/10
delta speed / delta time = 1
B
ds = 5 - 10
dt = 15 - 10
ds / dt = -5 / 5
ds / dt = -1
C
ds = 5 - 5
dt = 25 - 15
ds / dt = 0 / 10
ds / dt = 0
The average acceleration of A, B, and C will be 1 m/s², -1 m/s², and 0 m/s².
What is acceleration?An object is considered to have been accelerated if its velocity changes. Depending on whether an object is moving faster, slower, or in a different direction, its velocity may change. Examples of acceleration include a falling apple, the moon orbiting the earth, and a car that has stopped at a stop sign. These examples demonstrate how acceleration occurs whenever a moving object modifies its direction, speed, or both.
There are different types of acceleration :
Uniform accelerationNon-Uniform AccelerationAverage accelerationAverage acceleration is defined as the average change in velocity with respect to the average change in time.
SI unit is m/s² and it is vector quantity.
According to the question,
For A, Acceleration= (v₁-v₀)/(t₁-t₀)
⇒10-0/10-0
= 1 m/s².
For B, Acceleration= (v₃-v₂)/(t₃-t₂)
⇒5-10/15-10
= -1 m/s²
For C, Acceleration will be constant because change in velocity is constant, this is the case of uniform motion, so its acceleration is also going to be constant (as per the definition of acceleration change in velocity ratio change in time).
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i need help with these please
Answer:
Explanation:
question below................
Answer:
do your work why you in class and you would know
Explanation:
a. Block on a smooth incline.
A block of mass m= 3.8 kg on a smooth inclined plane of angle 36° is connected by a cord over a small frictionless
pulley to a second block of mass m2 = 3 kg hanging vertically. Take the positive direction up the incline and use 9.81 m/s2
for g.
What is the acceleration of each block to 1 decimal place?
Answer:
Explanation:
F = ma
3(9.81) - 3.8(9.81sin36) = (3 + 3.8)a
a = 1.10566...
a = 1.1 m/s²
the 3.8 kg mass will move up slope and the 3 kg mass will fall at that acceleration.
Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts steps of the same size from the front of the ship to the back. In terms of Emily's equal steps, what is the length of the ship
The length of the ship in terms of Emily's equal steps is 84.
The given parameters;
equal steps forward = 210equal steps backward = 42Defined parameters:
Let the constant velocity of the ship = VLet the velocity of Emily = VsLet the length of the ship = dLet the time of motion, = tThe velocity of Emily when moving forward in the direction of the ship:
[tex]V_s_1 = \frac{210}{t}[/tex]
The velocity of Emily when moving in opposite direction to the ship:
[tex]V_s_2 = \frac{42}{t}[/tex]
The constant velocity of the ship:
[tex]V = \frac{d}{t}[/tex]
Apply relative velocity formula to determine the length of the ship:
For forward (same direction) motion:
[tex](V_s_1 - V)t = d[/tex]
For backward (opposite direction) motion:
[tex](V_s_2 + V)t = d[/tex]
[tex](V_s_1 - V)t = (V_s_2 + V)t\\\\V_s_1 - V = V_s_2 + V\\\\\frac{210}{t} - \frac{d}{t} = \frac{42}{t} + \frac{d}{t} \\\\\frac{210}{t} - \frac{42}{t} = \frac{d}{t} + \frac{d}{t} \\\\\frac{210 - 42}{t} = \frac{d+ d}{t} \\\\\frac{168}{t} = \frac{2d}{t} \\\\2d = 168\\\\d = \frac{168}{2} \\\\d = 84[/tex]
Thus, we can conclude that the length of the ship in terms of Emily's equal steps is 84.
"Your question is not complete, it seems to be missing the following information;"
Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts 210 equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts 42 steps of the same size from the front of the ship to the back. In terms of Emily's equal steps, what is the length of the ship
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