A non-rotating spherical planet with no atmosphere has a mass M and radius R. A particle is fired off from the surface with a speed equal to 3/4 the escape speed. Calculate the farthest distance it reaches (measured from the center of the planet) if it is fired tangentially.

Answers

Answer 1

The farthest distance the particle reaches from the center of the planet is 14/3 times the radius of the planet.

When the particle is fired with a speed equal to 3/4 the escape speed, its initial kinetic energy will be half of the gravitational potential energy at the surface of the planet:

\(1/2 mv^2 = GMm/R\)

where m is the mass of the particle, v is its speed, G is the gravitational constant, and M and R are the mass and radius of the planet, respectively.

Solving for v, we get:

v = sqrt(2GM/R) × sqrt(1/2)

The escape speed from the surface of the planet is given by:

vesc = sqrt(2GM/R)

Therefore, the initial speed of the particle is:

v = 3/4 × vesc

Substituting this in the expression for v, we get:

v = sqrt(2GM/R) × sqrt(1/2) × 3/4

v = sqrt(GM/R) × sqrt(3/8)

The particle will follow a parabolic trajectory with the planet at the focus of the parabola. The farthest distance it reaches (measured from the center of the planet) occurs when it reaches the vertex of the parabola. The distance of the vertex from the focus is equal to the distance of the focus from the directrix, which is 2R.

Therefore, the farthest distance the particle reaches is:

d = 2R + r

where r is the distance of the focus from the vertex of the parabola. The distance r can be calculated using the equation for the parabolic trajectory:

\(r = 2GM/v^2\)

Substituting the expression for v, we get:

r = 8R/3

Therefore, the farthest distance the particle reaches is:

d = 2R + r = 8R/3 + 2R = 14R/3

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Related Questions

The number of protons plus the number of neutrons in an atom is equal to its

Answers

Answer:

Atomic Mass

Explanation:

Which of the following differentiates an audiologist from an anthropologist?
An audiologist uses empirical evidence to determine treatment.
An audiologist uses empirical evidence to determine treatment.

An audiologist examines physical characteristics of humans.

An audiologist evaluates communication methods.

An audiologist analyzes observed behaviors.

Answers

The statement that differentiates an audiologist from an anthropologist is that an audiologist examines physical characteristics of humans. That is option C.

Who is an audiologist?

Audiologist is an individual that specializes in the diagnosis, treatment and management of hearing loss and balance disorders in adults and children.

An anthropologist is also an individual that studied the past and present experiences of individuals.

Therefore, the statement that differentiates an audiologist from an anthropologist is that an audiologist examines physical characteristics of humans.

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Drag each label to the correct location. Sort the sentences based on whether they describe the properties of a heterogeneous or a homogenous mixture. Its components are visible. It may be mistaken for a pure substance. It can be separated using distillation. Concrete is an example of this kind of mixture.

Answers

Answer:

homo 1 3 hetero 2 4

Explanation:

As the hot gas from a space shuttle is released downward, what does this cause to happen?
A. The shuttle will explode.
B. Negligible force on the shuttle.
C. Downward force on the shuttle.
D. Upward force on the shuttle

Answers

Answer:

D. Upward force on the shuttle

Explanation:

The hot gas from space shuttles released downward causes an upward force on the shuttle and propels it up the more.

This hot gas is produced from super cooled oxygen and hydrogen tanks within the shuttle. The upward force on the shuttle allows the craft to escape the gravitational pull of the earth on the shuttle Special level of rapid acceleration must be attained for the shuttle to escape the earth pull.

The first step in responding to any sports injury is to __________.
A.
remove the danger that lead to the injury
B.
ensure that the player's air way is not obstructed
C.
begin chest compressions for CPR
D.
ask the player to stop playing the sport

Answers

Answer:

It would be A.

Explanation:

Ensuring the airway is not closed is second, and some times you may not need CPR, and you should already have told them to stop.

Answer:

A

Explanation:

just took the test

Which characteristics can be used to differentiate star systems? Select three options.
the number of stars in the system
O the level of dust and gas
the age of the stars in the system
the way stars are organized in the system
the color of stars in the system

Answers

Answer:

1,3and4 just did and got correct

Explanation:

Which characteristics can be used to differentiate star systems? Select three options.the number of stars

If you apply a force of 10 N to a table and push it 5 m in 10 s, how much power did you deliver? Multiple choice question. A) 50 W B) 25 W C) 500 W D) 5 W

Answers

Answer:

D) 5 W

Explanation:

Force=10N

Distance =5m

Time=10s

Power =?

But Power= Work done/Time taken

P= W/s

W= Fxd=10x5=50

P=50/10

P=5W

a node in the moon's orbit is where the moon's path crosses the

Answers

A node in the moon's orbit is where the moon's path crosses the ecliptic plane.

The moon's orbit around the Earth is not perfectly aligned with the Earth's orbit around the Sun. Instead, the moon's orbit is slightly inclined to the ecliptic plane, which is the plane of Earth's orbit around the Sun.

At two points in its orbit, the moon's path intersects or crosses the ecliptic plane. These points are known as the ascending node and the descending node. The ascending node is where the moon's path moves from below the ecliptic plane to above it, while the descending node is where the moon's path moves from above the ecliptic plane to below it.

The nodes are significant because they are the locations where lunar eclipses and solar eclipses can occur. A lunar eclipse occurs when the moon passes through Earth's shadow, and a solar eclipse occurs when the moon passes between the Sun and the Earth, casting a shadow on the Earth's surface. Eclipses can only occur when the moon is near one of its nodes.

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In calisthenics, the resistance is ultimately provided by __________. A. free weights B. springs and elastic bands C. gravity D. weight machines

Answers

When practicing calisthenics, the athlete's body is the only element that offers resistance. Thus, the resistance is ultimately provided by _gravity_. Option C is correct.

---------------------

Calisthenic is a physical discipline that is based only on the use of body weight.

It is a training system with physical activities that do not require any external element (weights, balls, cord). Gravity is the only force that exerts resistance.

This discipline develops strength, precision, and movement coordination, which are fundamental to increasing the difficulty of the exercises.

The athlete's body is the only element that offers resistance. Thus, the resistance is ultimately provided by _gravity_.

------------------------------

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Answer:

C

Explanation:

in the bohr model, what is the ratio of its kinetic energy to its potential energy?

Answers

Answer:

kinetic energy is half of the negative of potential energy.

Explanation:

The potential energy is the double of the negative of kinetic energy.

ocean currents are caused primarily by the gravitational attraction between the earth, moon, and sun. true or false

Answers

The statement that ocean tides are caused primarily by the gravitational attraction between the earth, moon, and sun is a true statement.

Tides can be defined as the rise and fall of water level in water bodies such as lakes and oceans due to the gravitational force of attraction exerted by the moon on earth. The side closest to the moon creates a bulge of water known as high tide. Low tides are generally experienced when a sea level is not within the bulge.

Generally, the gravitational pull of the Moon cause visible changes on planet Earth's surface.

This ultimately implies that, the pull of the Moon's gravity causes high and low tides on planet Earth's surface.

Therefore, The statement that ocean tides are caused primarily by the gravitational attraction between the earth, moon, and sun is a true statement.

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Which condition must be met in order for an equation to be balanced?

Answers

Answer:

There must be an equal amount of each element on both sides of the equation. Hope this helps and please marks as the brainliest.

Explanation:

Answer:

The answer is D

Explanation:

Hope this helps!

1,3-butadiene undergoes an electrophilic addition with hbr. Complete the steps in the mechanism to produce the product shown.

Answers

There are two products of the addition of HBr to butadiene.

What is an addition reaction?

An addition reaction is a reaction in which a compound is added across the double bond. We must recall that the compound 1,3-butadiene is a conjugated double bond hence the final products are controlled by resonance effects.

The mechanism of the addition of HBr to 1,3-butadiene  is shown in the image attached to this  answer.

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1,3-butadiene undergoes an electrophilic addition with hbr. Complete the steps in the mechanism to produce

please help me please please, i will brainliest the right answer

Answers

help with whatttt? there’s nothing

The orbits of stars around the center of the Milky Way Galaxy suggest that the mass at the center of the Galaxy is about 4 million solar masses. What is believed to be the diameter of this supermassive object?
a. smaller than Earth's orbit
b. about 8 ly
c. smaller than the diameter of the Sun
d. about half a parsec

Answers

It is estimated that the supermassive object at the Milky Way Galaxy's center has a diameter of  (Choice d) around half a parsec.

Based on the orbits of stars around the center of the Milky Way Galaxy, it is estimated that the mass at the center is approximately 4 million solar masses.

The diameter of the supermassive object, known as the galactic nucleus or black hole, is believed to be about half a parsec. A parsec is a unit of distance equal to approximately 3.26 light-years.

Therefore, the diameter of this supermassive object is larger than Earth's orbit (option a), about 8 light-years (option b), and smaller than the diameter of the Sun (option c).

The estimated diameter of about half a parsec suggests a relatively compact but incredibly massive object at the center of our galaxy. Thus, option d is the correct answer.

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what is the maximum acceleration of a platform that oscillates at amplitude 2.40 cm and frequency 9.90 hz?

Answers

The maximum acceleration of a platform is 92.7 m/s².

What is an oscillation?

Oscillation is the process of any quantity or measure repeatedly varying about its equilibrium value in time. A periodic variation of a substance between two values or around its center value is another definition of oscillation.

We know,

The acceleration amplitude = \(a_{m}\) = ω²\(x_{m}\)

Here,

ω = angular frequency (ω=2\(\pi\)f)

There are 2\(\pi\) radians in one cycle, so we obtain:

\(a_{m}\) = ω²\(x_{m}\) = (2\(\pi\)f)²\(x_{m}\) = (2\(\pi\)(9.90Hz)²(0.024m) = 92.7 m/s².

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What does intensity mean in relation to Fitt )?

Answers

the intensity of exercise undertaken or how hard you exercise.

Please I need help asap it due today!!!

In Racial Formations by Michael Omi and Howard Winant, race is defined as a socio historical concept, what does that mean
to the authors? Explain how race is
socially constructed or strictly biological. Support your response with two paragraphs.

Answers

The concept of race as a socio-historical construct highlights the importance of understanding the social, political, and economic contexts in which race is created and maintained.

What is race?

According to Michael Omi and Howard Winant, in "Racial Formations," race is a socio-historical concept that is constructed through the intersection of cultural, political, and economic forces.

In this book, they argue that race is not an immutable, biologically determined characteristic of individuals or groups but rather a social construct that is created and maintained through systems of power and inequality.

The authors illustrate how race is constructed through examples from different historical periods and social contexts.

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why is the voltage of the two batteries connected in parallel the same as the voltage of each battery measured separately

Answers

The process of connecting batteries in parallel involves linking all their positive terminals together and similarly for their negative ones. Such an arrangement guarantees that there is no variation in the voltage discrepancy between every battery's polar ends.

What is parallel connection?

Parallel connection is an electrical arrangement that involves connecting circuit components to a common voltage source in multiple pathways. Typically, two common points link these components with one another. The primary objective of such setups is enhancing current flow within circuits by providing more channels for current to travel through.

Each component in these configurations experiences identical voltage values without any change; however, differing currents per component exist at various times during their usage cycle. Nevertheless, all individual currents converge into a single total current flowing through the entire circuit.

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the wind is blowing at 55 m/s from the north. a pilot wishes to fly a plane at 130m/s 60 south of east with respect to the ground. find the airspeed and the heading of the plane.

Answers

To find the airspeed and heading of the plane, we can use vector addition and trigonometry. Let's break down the motion into its components:

The wind is blowing at 55 m/s from the north. We can represent this velocity as (0 m/s, -55 m/s) in Cartesian coordinates.The pilot wants to fly the plane at an airspeed of 130 m/s 60° south of east. We need to find the components of this velocity. The east component is given by 130 m/s * cos(60°) = 65 m/s, and the south component is given by 130 m/s * sin(60°) = -112.5 m/s.Now, we can add the velocities of the wind and the plane to get the resultant velocity: Resultant velocity = (0 m/s + 65 m/s, -55 m/s - 112.5 m/s) = (65 m/s, -167.5 m/s)

The magnitude of the resultant velocity gives us the airspeed of the plane: sqrt((65 m/s)^2 + (-167.5 m/s)^2) ≈ 178.85 m/s.

To find the heading of the plane, we can use trigonometry. The angle between the resultant velocity vector and the positive x-axis is given by atan((-167.5 m/s) / 65 m/s). Calculating this angle gives us approximately -69.5°.However, since the plane is south of east, we need to subtract this angle from 90° to find the heading:

Heading = 90° - 69.5° = 20.5°.

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Explain the difference between velocity and acceleration.​

Answers

Answer:

velocity has direction and acceleration doesn't

Acceleration is increasing or decreasing speed or changing direction, whereas velocity is how much distance you cover in a given amount of time.

Please help me
Do the file bellow
I will choose Brainlest
50 points for sale

Answers

Answer:

It could not be opened, sorry.

Which of the following scientists won a Nobel Prize for pioneering work in the
study of fiber optics?
O A. Marie Sklodowska-Curie
B. Warren Washington
O C. Charles Kuen Kao
D. Subrahmanyan Chandrasekhar

Answers

Scientists  who won a Nobel Prize for pioneering work in the study of fiber optics is Charles Kuen Kao. Hence, option C is correct.

What is fiber optics ?

Fiber optics is the study of technologies that transmit information as light pulses along a plastic or glass fiber. Thin glass fibers or filaments have been used to view inside the body since the 1930s, but they have long been deemed unsuitable for transmitting information over long distances because too much light is wasted in the process.

Charles Kao offered a solution in the 1960s: highly pure glass fibers could convey enough light. His invention has made optical fiber telecommunication practicable when combined with laser technology.

Charles Kao won the Nobel price in physics in 2009 for the groundbreaking achievements concerning the transmission of light in fibers for optical communication.

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Please help! Timed! I would really appreciate it ill try to give brainliest!
Amy doesn't want to be late for class so she rushes to McDonalds at lunch. How much time would it take Amy to walk 2km to the restaurant for an apple pie if she walked at a rate of 4.5km/h? *

.44 m/s
.44 hr or 26.6 minutes
.44 hr/m or 2.66 minutes

Answers

Answer:

i believe it is .44 hr o26.6!

Explanation:

is the opposition to ac current flow caused by a capacitor.

Answers

No, the opposition to AC current flow is not caused by a capacitor. Rather, it is caused by the inductance of a coil or the resistance of a resistor.

The opposition to AC current flow is called impedance. Capacitors, like resistors and inductors, contribute to the total impedance of a circuit. However, the impedance of a capacitor does not cause opposition to AC current flow, rather it acts to store and release energy in the circuit.  A capacitor opposes the flow of direct current (DC), however, when it is placed in a circuit with AC, it charges and discharges as the current alternates. This results in a phase shift between the voltage and current, causing a reactive component to the circuit impedance which is called capacitive reactance (Xc).

This is the property of the capacitor to store electrical energy in an electric field, and when the electric field is discharged, it releases that energy into the circuit. Capacitance is an important factor in many types of circuits such as filters, power supplies, and timing circuits. In conclusion, capacitors do not cause opposition to AC current flow, rather they contribute to the total impedance of a circuit and play an important role in many electrical circuits.

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Yes, the opposition to AC current flow is caused by a capacitor. It is also known as capacitance opposition or capacitive reactance. Capacitance is the ability of a capacitor to store electrical charge, and it opposes a change in voltage.

When an alternating current (AC) passes through a capacitor, the charges present on the plates will be equal and opposite in direction. This means that the capacitor will oppose any change in voltage, resulting in a phase difference between the voltage and the current. When a capacitor is connected to an AC source, the current will be initially high, and the voltage will be low because the capacitor opposes any change in voltage.

As the AC voltage reaches its peak, the current decreases to zero because the capacitor is fully charged. When the voltage starts to decrease, the capacitor discharges, and the current starts to flow in the opposite direction. The opposition of a capacitor to AC current flow is measured in units called ohms and is known as capacitive reactance.

The formula for calculating capacitive reactance is: Xc = 1/(2πfC), Where: Xc = Capacitive reactance f = Frequency of the AC source C = Capacitance of the capacitor. So, in summary, the opposition to AC current flow is caused by a capacitor because of its ability to store electrical charge. This opposition is known as capacitive reactance and is measured in ohms.

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A metal cube has a mass of 10 grams, and occupies 5 cubic centimeters of space.
What's its density?

Answers

Answer:

ρ (density) = M / V         mass / unit volume

ρ = 10 g / 5 cm^3 = 2 g/cm^3        density of the metal

If the coefficient of static friction at all contacting surfaces is determine the inclination at which the identical blocks

Answers

The tangent of the angle at which the items slide equals the coefficient of static friction. The measurement of k can be done in a similar way. To accomplish it, push the upper object while angling it upward. The tangent of that angle equals k when the upper object slides along at a constant speed.

Why is the coefficient of static friction determined using an incline?

By calculating the angle at which the force of gravity overcomes the static friction, you can utilize an item that is inclined to calculate the static coefficient of friction.

How can you tell which way static friction is prevailing?

Static friction pushes in the direction you're trying to travel when you walk (see Figure 2 below). In the absence of friction, the foot would slip backwards as it presses on the ground (like walking on ice).

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12. The diameter of a circle is 2.42m. Calculate its
area in proper significant figure​

Answers

Answer:

A = 4.6 [m²]

Explanation:

The area of a circle can be calculated by means of the following equation.

\(A=\frac{\pi }{4} *D^{2}\)

where:

A = area [m²]

D = diameter = 2.42 [m]

Now replacing:

\(A=\frac{\pi }{4} *(2.42)^{2} \\A = 4.6 [m^{2} ]\)

What is necessary to move an object from one side of a room to the other side of the room? (Select all that apply.)
A) force needs to be applied to the object.
B) The weight needs to be determined. |
C) The object must be set in motion.
D) The person must know the position of the object.

Answers

For moving an object from one side of a room to the other side of the room a force is needed to be applied to the object and the position of the object must be known. Thus, A and D are the correct options.

What is Motion?

Motion is a phenomenon in which an object changes its position with respect to time. It is the distance or displacement covered by an object in a particular time period.

Newton's first Law states that a body at rest will stay at rest and a body in motion will remain in motion unless and until an external force is applied on it. Force is responsible for the displacement of an object from one place to another.

Direction is equally important in motion as force applied in the direction opposite to the motion can stop the motion while the force in the direction of motion can accelerate the motion.

Therefore, correct options are A and D. The force and position are important factors for the motion of an object.  

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assume that i = 10 a . (figure 1) you may want to review (pages 803 - 806). What is the magnetic field strength at point b? Express your answer to two significant figures and include the appropriate units.

Answers

The magnetic field strength at point b can be determined by applying Ampere's law and considering the current flowing through the wire. The answer should be expressed with two significant figures and appropriate units.

To find the magnetic field strength at point b, we can use Ampere's law, which states that the magnetic field around a closed loop is directly proportional to the current passing through the loop.

In Figure 1, if a current of 10 A is flowing through the wire, we can consider a circular loop centered at point b with a radius r. Applying Ampere's law, we have:

B * 2πr = μ₀ * I_enc

where B is the magnetic field strength at point b, μ₀ is the permeability of free space, I_enc is the current passing through the loop enclosed by the circular path, and 2πr is the circumference of the loop.

Since point b is located on the wire, the circular loop will enclose the entire current I. Therefore, I_enc = I = 10 A.

Rearranging the equation, we have:

B = (μ₀ * I_enc) / (2πr)

To obtain the magnetic field strength at point b, the radius r needs to be specified. Without the specific value for r, we cannot provide an exact numerical answer. It is important to know the radius to calculate the magnetic field strength accurately.

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