You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of o=2.45 km/s
. The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth.

With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is E=6370000 m
, the mass of the Earth is E=5.98×1024 kg
, the acceleration due to gravity on the surface of the Earth is =9.81 m/s2
and the universal gravitational constant is =6.67×10−11 N·m2/kg2
.

The magnitude of acceleration at the given point is 8.04 m/s², and the direction of acceleration at the given point is 38.5° below the negative x-axis.

To find the magnitude of acceleration at the given point, we need to calculate the force acting on the block using the potential-energy function and then use Newton's second law, F=ma, to find the acceleration.

The force acting on the block can be found by taking the negative gradient of the potential-energy function;

F = -∇U = (-∂U/∂x)i + (-∂U/∂y)j

where i and j are unit vectors in the x and y directions, respectively.

Taking the partial derivatives of U(x,y) with respect to x and y, we get;

∂U/∂x = 11.0 J/m² × x

∂U/∂y = -11.1 J/m³ × y₂

Plugging in the values x=0.40 m and y=0.50 m, we get;

∂U/∂x = 1.76 J/m

∂U/∂y = -1.39 J/m

Therefore, the force acting on the block at (0.40 m, 0.50 m) is;

F = (-1.76 J/m)i + (-1.39 J/m)j

Using Newton's second law, F=ma, we can find the magnitude of acceleration:

a = F/m = ([tex]F_{x}[/tex][tex]F_{y}[/tex]/m₂ + [tex]F_{y}[/tex]₂/m₂)1/2

= [(1.76 J/m)2 + (-1.39 J/m)2]/0.0400 kg

= 8.04 m/s2

Therefore, the magnitude of acceleration at the given point is 8.04 m/s².

To find the direction of acceleration at the given point, we need to find the angle between the force vector and the positive x-axis.

The angle θ can be found using the formula;

θ = tan-1([tex]F_{y}[/tex] /[tex]F_{x}[/tex])

Plugging in the values of [tex]F_{x}[/tex] and [tex]F_{y}[/tex] at (0.40 m, 0.50 m), we get;

θ = tan-1(-1.39 J/m / 1.76 J/m)

= -38.5°

Since the force vector is in the third quadrant (i.e., both [tex]F_{x}[/tex] and [tex]F_{y}[/tex] are negative), the angle θ is negative. Therefore, the direction of acceleration at the given point is 38.5° below the negative x-axis.

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For mass-containing things, it is impossible to move at or faster than the speed of light. Potential drawbacks include length contraction, time dilation, mass gain, gravitational effects, and high energy demands.

If an object could ever move at the speed of light, its mass would become infinite. The required energy would therefore have to be infinite, which is not possible.

The risk to other road users increases as you drive faster. Overspeeding cars put pedestrians in a very dangerous situation. Driving too quickly uses more fuel. After the speed reached a certain point, fuel usage skyrocketed.

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Answer:

Explanation:

To find the relative velocity of two cars moving in different directions, we need to subtract their velocities. In this case, one car is moving with a velocity of 70 km/hr and the other car is moving with a velocity in the west direction.

Let's assume that the velocity of the second car is also 70 km/hr. Since the car is moving in the west direction, we can represent its velocity as -70 km/hr (negative sign indicates motion in the opposite direction).

Now, we can find the relative velocity of the second car with respect to the first car by subtracting the velocity of the first car from the velocity of the second car:

Relative velocity = Velocity of the second car - Velocity of the first car

= (-70 km/hr) - (70 km/hr)

= -140 km/hr

Therefore, the relative velocity of the second car with respect to the first car is -140 km/hr, which means that the two cars are moving away from each other at a speed of 140 km/hr.

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The fulcrum to balance the meter stick should be placed 8.33 cm to the left of the center of mass of the meter stick, under the condition that the mass of the meter stick is 0.2 kg and its center of mass is located at its geometric center.

In order to balance the meter stick with the 1.3 kg mass placed to the left end, we have to evaluate the distance ‘d' from the center of mass of the meter stick to the fulcrum.

The given center of mass of the meter stick is found at its geometric center which is at 50 cm from either end of the stick. Then the mass of the meter stick is 0.2 kg.

We can apply the principle of moments to evaluate this problem. The principle of moments says that for an object in equilibrium, the summation of the clockwise moments about any point must be equivalent to the sum of the anticlockwise moments about that point.

Let us consider that moments about the fulcrum. The clockwise moment because of the weight of the 1.3 kg mass and is stated by (1.3 kg) x (d cm). The anticlockwise moment is because of the weight of the meter stick and is given by (0.2 kg) x (50 - d cm). Since the meter stick is balanced, these two moments should be equal.

(1.3 kg) x (d cm)

= (0.2 kg) x (50 - d cm)

Evaluating for‘d’,

d = 8.33 cm

Hence, the fulcrum should be placed 8.33 cm to the left of the center of mass of the meter stick.

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A convex lens is also known as a converging lens because it causes the incident light rays that are travelling parallel to its main axis to converge.

A convex lens has an outward curvature. In comparison to the edges, the middle is thicker. The rays of light bend in the direction of one another when they travel through a convex lens. On the other side of the lens, the rays only come together at one location. Convex lenses amplify or provide the impression that objects are larger.

The image is upside down in relation to the original object and is also oriented inverted from right to left in the convex lens. The term "inverted" refers to such a position. The real image formed by the convex lens is inverted.

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As the pendulum swings from position A to position B, the potential energy decreases while the kinetic energy increases. According to the law of conservation of energy, the total energy in a system remains constant, neglecting friction. Therefore, the potential energy lost by the pendulum is converted into kinetic energy. The correct relationship of kinetic energy to potential energy as the pendulum swings from position A to position B is:

The potential energy decrease is equal to the kinetic energy increase.

So, the answer is option B.

Answer:

The potential energy increase is equal to the kinetic energy decrease.

Answer:

W = 6000 Joule

Explanation:

Work is defined as force times distance

W = F * d

We know that F = 15N, we just need the distance (d)

Imagine you have a square lawn with length of 10 m and width of 20m. So, we want to know the the distance you have to travel to cover every square meter of the lawn.

The width of the mower is only 50 cm = 0.5 m.

This means that you have to go back and forth 40 times to cover 20m (lawn width), with a distance of 10 m (lawn length). So,

d = 10 (meter) * 40 (times) = 400 meter

Therefore:

W = (15) * (400) = 6000 J

Answer:

Potential Difference = Voltage =  Resistance * Current

As long the resistance is a constant the PD will be a straight line when plotted against the current.

Answer:

Approximately [tex]5.94\; {\rm N}[/tex].

Explanation:

The gravitational force between two objects of uniform mass is:

[tex]\displaystyle F = \frac{k\, M\, m}{r^{2}}[/tex],

Where:

Rearrange this equation to find [tex]r[/tex]:

[tex]\begin{aligned} r &= \sqrt{\frac{k\, M\, m}{F}} \\ &= \sqrt{\frac{(6.67 \times 10^{-11})\, (75.0)\, (60.0)}{8.50 \times 10^{-9}}}\; {\rm kg} \\ &\approx 5.94\; {\rm kg}\end{aligned}[/tex].

The question is incomplete, I think the question is:

You decide to use your body as a Carnot heat engine. The operating gas is in a tube with one end in your mouth (where the temperature is 37.0 ∘C) and the other end at the surface of your skin, at 30.0 ∘C.(a) What is the maximum efficiency of such a heat engine? Would it be a very useful engine? (b) Suppose you want to use this human engine to lift a 2.50kg box from the floor to a tabletop 1.20m above the floor. How much must you increase the gravitational potential energy, and how much heat input is needed to accomplish this? (c) How many 350-calorie (those are food calories, remember) candy bars must you eat to lift the box in this way? Recall that 80% of the food energy goes into heat.

We need to input about 1278 J of heat into the heat engine to lift the box, and we need to eat about 1.09 candy bars to lift the box

The Carnot heat engine is an idealized thermodynamic cycle that operates between two heat reservoirs and achieves the maximum possible efficiency. It is a theoretical model used to study the behavior of real-world heat engines and provides a benchmark for their performance.

a) The maximum efficiency of a Carnot heat engine is given by the equation:

η = 1 - Tc/Th

where η is the efficiency, Tc is the temperature of the cold reservoir (in this case, 30.0 °C), and Th is the temperature of the hot reservoir (in this case, 37.0 °C).

Plugging in the numbers, we get:

η = 1 - 303 K/310 K ≈ 0.023 or 2.3%

This is a very low efficiency, and the heat engine would not be very useful for doing work.

b) To lift a 2.50 kg box from the floor to a tabletop 1.20 m above the floor, we need to increase its gravitational potential energy by:

ΔPE = mgh

where m is the mass of the box, g is the acceleration due to gravity (9.81 m/s^2), and h is the height the box is lifted.

Plugging in the numbers, we get:

ΔPE = (2.50 kg)(9.81 m/s^2)(1.20 m) ≈ 29.4 J

To accomplish this, we need to input heat Q into the heat engine. Since the efficiency of the heat engine is only 2.3%, the amount of heat needed is:

Q = ΔPE/η = (29.4 J)/(0.023) ≈ 1278 J

So we need to input about 1278 J of heat into the heat engine to lift the box.

c) To input 1278 J of heat into the heat engine, we need to consume food with a total energy content of:

E = Q/ηfood

where ηfood is the efficiency of converting food energy into heat energy. Since 80% of the food energy goes into heat, we have:

ηfood = 0.80

Plugging in the numbers, we get:

E = (1278 J)/(0.80) ≈ 1598 J

To convert this energy content into calories, we divide by 4.184 J/cal, giving:

E = 381 cal

Finally, to determine the number of 350 calorie candy bars needed, we divide the total energy content by the energy content per candy bar:

N = E/Ebar

where Ebar is the energy content of a single candy bar (350 cal). Plugging in the numbers, we get:

N = (381 cal)/(350 cal/bar) ≈ 1.09 bars

So we need to eat about 1.09 candy bars to lift the box.

Therefore, To lift the box, we must put approximately 1278 J of heat into the heat engine and consume approximately 1.09 candy bars.

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Answer: The force of gravity, or gravitational force, pulls objects with mass toward each other.

We often think about the force of gravity from Earth. This force is what keeps your body on the ground.

But any object with mass exerts a gravitational force on all other objects with mass. For example, there is a gravitational force between you and every object around you.

The gravitational force between two objects is larger when the masses of the objects are larger. That’s why you can feel the gravitational force between you and Earth, but the force between you and objects with smaller masses is too weak to feel.

The gravitational force between two objects also depends on the distance between their centers. The further objects are from one another, the weaker the force is.

The position of center of mass is, 1 cm right, and 1.4 cm above the corner A, of the square ABCD.

The respective coordinates of masses, on corner ABCD, are:

Let the coordinates of COM(center of mass), be, Xcom and Ycom.

Therefore,

Xcom = [ ∑([tex]M_{i}[/tex] x [tex]X_{i}[/tex]) / ∑([tex]M_{i}[/tex]) ] , and

Ycom = [ ∑([tex]M_{i}[/tex] x [tex]Y_{i}[/tex]) / ∑([tex]M_{i}[/tex]) ]

That is,

Xcom = [ {(2x0)+(4x2)+(6x2)+(8x0)} / (2+4+6+8) ]

Xcom = (20/20) cm

Xcom = 1cm

Similarly,

Ycom = [ {(2x0)+(4x0)+(6x2)+(8x2)} / (2+4+6+8) ]

Ycom = (28/20) cm

Ycom = 1.4 cm

So, the position of center of mass is, 1 cm right, and 1.4 cm above the corner A, of the square ABCD.

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Answer: Doubled

Explanation:

Answer: Voltage

Explanation: Not really sure what all that other stuff is after your question...

The "force" that moves electric charge carriers through an electric circuit is ________.

An electric charge carrier moving through a circuit is a charged particle (usually electrons). The force that pushes it is called an electromagnetic force, commonly known as EMF.

Between atoms, EMFs are what attract electrons from one atom to another to form bonds. Likewise, In a circuit, the EMF is the driving force, which is known as voltage.

Superconductivity refers to a state in which these charge carriers travel at a specific voltage with no resistance, meaning no energy is lost. However, this isn't an independent force, so it's incorrect.

Resistance affects the circuit by slightly dampening the flow of charge carriers. Resistance commonly comes in the form of temperature or simply a characteristic of the material through which the circuit flows, so this is incorrect.

Current merely refers to the flow of charge carriers through a circuit in a given time window.

(Think of a circuit as a water pipe. Current is like the speed of a specific amount of water and Voltage (or EMF) is the pressure in the pipe. The higher the pressure, the faster the water flows. Resistance is anything in the pipe that impedes the water flow)

The time taken for the cordial to freeze is 267.2 s.

The amount of heat energy (Q) required to freeze the cordial can be calculated using the following formula:

Q = ml

where;

Q = 334 J/g x 200 g

Q = 66,800 J

The time taken for the cordial to freeze is calculated as;

t = Q/W

where;

t = (66,800 J) / (250 J/s)

t = 267.2 s

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13. If the supply of gasoline rises, a substitute that may increase in demand could be electric or hybrid vehicles.

14. Here is how each of the following events may have affected the world price of oil using basic supply and demand analysis:

a. Tax credits offered for expenditures on home insulation would likely decrease the demand for oil as people would use less energy to heat their homes. This would lead to a decrease in the price of oil.

b. The completion of the Alaskan oil pipeline would increase the supply of oil, leading to a decrease in the price of oil.

c. The discovery of oil in Mexico and the North Sea would increase the supply of oil, leading to a decrease in the price of oil.

d. The popularity of Sport Utility Vehicles and minivans would increase the demand for oil as these vehicles typically consume more gasoline than smaller cars. This would lead to an increase in the price of oil.

e. The depletion of natural oil reserves would decrease the supply of oil, leading to an increase in the price of oil.

The new potential energy you will have, given that your height is doubled is 114 J

The following data were obtained from the question:

The new potential energy can be obtained as illustrated below:

PE₁ / h₁ = PE₂ / h₂

57 / H = PE₂ / 2H

Cross multiply

57 × 2H = PE₂ × H

Divide both sides by H

PE₂ = (57 × 2H) / H

PE₂ = 57 × 2

PE₂ = 114 J

Thus, from the above calculation, we can conclude that the new potential energy is 114 J

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Answer: The mass has no velocity when kinetic energy=0.

Explanation: K=1/2mv^2 so if K=0, velocity must also equal 0.

Answer:

Step 1: Given data

Acceleration due to gravity on the surface of the earth is g.

The radius of the earth is R and x is the height of the satellite above the earth's surface.

The mass of the satellite is m.

Step 2: Calculate the orbital speed of the satellite.

We know that,

mv2R+x=GMmR+x2

v=GMR+x

v=GMR2×R2R+x

Step 3: Final answer

v=gR2R+x

We can also write it as

v=gR2R+x12

The air becomes humid during warm front passes and a cold front means a transition where warm air is being replaced by the cold air.What do you mean by weather?

The weather means the atmosphere at a particular place and time with respect to temperature, pressure, cloudiness, wind, etc.

A warm front means when the air is very warm and humid as compared to before.

A cold front is when the air is very colder and drier than the air above it. More than 15 degrees temperature can drop down when a cold front passes.

A cold front will probably bring winds, thunderstorms, and rain.Therefore, the cold front moves faster than the warm front.Learn more about the Weather here:

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The initial speed of the cannon was 2 m/s.

The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the cannon and the cannonball form a closed system, and no external forces are acting on it. Therefore, the total momentum of the system before and after the firing must be equal.

According to the law of conservation of momentum, the total momentum of the cannon and the cannonball must be conserved before and after the firing. Therefore, we can use the equation:

m(cannon) * v(cannon) = m(cannonball) * v(cannonball)

where m is the mass and v is the velocity.

Substituting the given values, we get:

500 kg * v(cannon) = 10 kg * 100 m/s

Solving for v(cannon), we get:

v(cannon) = 2 m/s

As a result, the cannon's starting speed was 2 m/s.

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The time takes  is 1.19 ms for the sound waves to travel the length of the aluminum rod between the two houses.

The speed of sound in aluminum can be determined utilizing the condition

v = sqrt(Y/ρ),

where Y is the Youthful's modulus and ρ is the thickness of the material. Connecting the qualities for aluminum, we get

v = [tex]sqrt(6.9x10^10 N/m^2/2700 kg/m^3) = 5110 m/s[/tex].

The time it takes for the sound waves to venture to every part of the length of the aluminum pole can be determined utilizing the condition

t = d/v,

where d is the distance and v is the speed of sound. Connecting the qualities, we get

t = 6.1 m/5110 m/s = 0.00119 s or 1.19 ms.

Subsequently, it takes 1.19 ms for the sound waves to venture to every part of the length of the aluminum bar between the two houses.

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Answer:

Explanation:

B.  W = mg     m = W/g = (650 N)/(9.8 m/s²) = 66.33 kg

C.  Ff = μN = (0.12)(650 N) = 78 N

D.  F > 78 N

Note:  Brainly doesn't provide drawing tools, so I can't help you with the FBD.  But here's a try at it: N = normal force, F = applied force, W = weight of person + sled, Ff = force of friction,  ⊕ (person and the sled)

       N

       ↑

Ff←   ⊕  →F

       ↓

      W

The stone possesses potential energy at the top of the cliff, which is converted to kinetic energy as it falls toward the ground. Using the formula for the distance traveled by a freely falling object, we can calculate that the height of the cliff is 20 meters. The ground height is equal to zero, and when the stone is halfway down, it has a kinetic energy of 100 Joules. Using the formula for the final velocity of a freely falling object, we can calculate that the stone's final velocity as it strikes the ground is 20 m/s.

(a) The form of energy possessed by the stone before it falls is potential energy. When the stone is at the top of the cliff, it has the potential to do work due to its position relative to the ground. This potential energy is converted into kinetic energy as the stone falls towards the ground.

(b) We can use the formula for the distance traveled by a freely falling object to determine the height of the cliff:

d = 1/2 * g * t^2

where d is the distance, g is the acceleration due to gravity, and t is the time taken to fall.

Substituting the given values, we get:

d = 1/2 * 10m/s^2 * (2s)^2

d = 20 meters

Therefore, the height of the cliff is 20 meters.

(c)

(i) The ground height h is equal to zero since it is the reference level.

(ii) When the stone is halfway down, it has fallen a distance of d/2 = 10 meters. At this point, all of the potential energy has been converted to kinetic energy. We can use the formula for kinetic energy to calculate the kinetic energy of the stone:

KE = 1/2 * m * v^2

where KE is the kinetic energy, m is the mass of the stone, and v is its velocity.

Substituting the given values, we get:

KE = 1/2 * 2kg * (2 * g * d/2)

KE = 100 Joules

Therefore, the kinetic energy of the stone when halfway down is 100 Joules.

(iii) To find the final velocity of the stone as it strikes the ground, we can use the formula for the final velocity of a freely falling object:

v = sqrt(2 * g * d)

where v is the final velocity, g is the acceleration due to gravity, and d is the distance fallen.

Substituting the given values, we get:

v = sqrt(2 * 10m/s^2 * 20m)

v = sqrt(400)

v = 20 m/s

Therefore, the final velocity of the stone as it strikes the ground is 20 m/s.

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From the table, we can see that Charlene will have the most profit ($21) when she walks 3 dogs per month, charging $9 per walk.

Based on the provided data, we can create a demand schedule for the prices and the quantity demanded per month.

Let's first organize the data in a table:

Price ($) Quantity Demanded per Month

15 1

12 2

9 3

6 5

3 7

If you plotted these numbers on a graph, you would expect to see a downward-sloping curve, illustrating the inverse relationship between price and quantity demanded. As the price decreases, the quantity demanded per month increases.

Now let's consider Charlene's costs and profits from walking dogs. It costs her $2.00 for each bus ride to the dog owner's house.

To calculate her profit, we need to find her total revenue at each price point, then subtract her total costs.

Price ($) Quantity Demanded per Month Total Revenue ($) Total Costs ($) Profit ($)

15 1 15 2 13

12 2 24 4 20

9 3 27 6 21

6 5 30 10 20

3 7 21 14 7

From the table, we can see that Charlene will have the most profit ($21) when she walks 3 dogs per month, charging $9 per walk.

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The change in momentum of the object in terms of its mass, initial velocity, and final velocity is 5 kg m/s.

The change in momentum of an object can be calculated using the formula:

Δp = m * (v - u)

In this case, the mass of the object is 0.5 kg, the initial velocity (u) is 0 m/s, and the final velocity (v) is 10 m/s after 3 seconds of uniform acceleration.

Substituting these values into the formula gives:

Δp = 0.5 kg * (10 m/s - 0 m/s)

Δp = 5 kg m/s

Therefore, the change in momentum of the object in terms of its mass, initial velocity, and final velocity is 5 kg m/s.

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--The complete Question is, A 0.5 kg object is initially at rest. It then accelerates uniformly for 3 seconds and reaches a velocity of 10 m/s. Calculate the change in momentum of the object in terms of its mass (m), initial velocity (u), and final velocity (v).--

Ans. 0.75

To convert watts into kilowatts we must divide it by 1000

so dividing 750W by 1000

we get,

750/1000 = 0.75

hence 750W in kilowatts equals to 0.75

Answer:

Melting Point = -50 °C

Boiling Point = 50 °C

Explanation:

A heating curve displays a substance in its 3 states.

On the graph, each region where the slope is positive represents the substance as a solid, liquid, or gas.

When the slope is 0, this is the temperature point at which the substance's state of matter has changed (i.e., melting or boiling/vaporization point) – also known as a phase transition. Essentially, the 0 slope regions are where the substance is changing from one state of matter to the next.

(When the substance is being heated, it's absorbing energy, but when it reaches a phase transition point, the substance begins to consume energy to change its matter state. That's why the temperature doesn't go up while the substance's internal Energy increases.)

In (Figure 1), where 'x' is Energy (J) and 'y' is Temperature (°C):

Region A (0 J ≤ x ≤ 200 J):

The slope is positive, so the substance is in a constant matter state. Because it's the first sloped region, the substance is in its solid state from -100 °C to -50 °C.

Region B (200 J ≤ x 600 J):

The slope is 0, so the substance has reached a phase transition point. Because the previous region was when the substance was solid, that means that the temperature throughout Region B is the melting point at -50 °C.

Region C (600 J ≤ x ≤ 800 J):

The slope is positive so the substance is in a constant matter state. We've already identified when the substance was solid and when it melted, so now the substance is in its liquid state from -50 °C to 50 °C.

Region D (800 J ≤ x ≤ 900 J):

The slope is 0, and since the previous region was when the substance was a liquid, it's now reached its boiling point at 50 °C.

Region E (900 J ≤ x ≤ 1000 J):

The slope is positive, and we've previously identified all of the transition points and matter states except for one, so the substance is now in its gaseous state after reaching 100°C.

(Once a substance reaches its gaseous state, the Temperature/Energy ratio is constant.)

Answer:60 seconds

Explanation: Since we have the boy's initial location si (0m), final location sf (600m) and his velocity v, we can have our position equation like so:

sf = si + vt
600 = 0 + 10t

Solve for t by dividing 600 by 10 and your time t = 60s

To determine the elemental composition of the faraway galaxy, would use spectroscopy to analyze the light that is emitted or absorbed by the galaxy. This technique enables me to determine the types of atoms and molecules that are present in the galaxy, providing insights into its elemental composition.

To determine the galaxy's motion relative to the Milky Way, would use the Doppler effect to measure the galaxy's redshift or blueshift. This would enable me to determine whether the galaxy is moving away from or towards us, and at what speed, providing information about its motion relative to our galaxy.

It could also look for any gravitational lensing effects, which could indicate the presence of massive objects that are influencing the galaxy's motion.

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