The molar specific heat of a diatomic gas is measured at constant volume and found to be 29.1 J/mol .K. What are the types of energy that are contributing to the molar specific heat? (a) translation only (b) translation and rotation only (c) translation and vibration only (d) translation, rotation, and vibration

Answer:

It's one meter long and has 100 cm and 39.4 inchs

Explanation:

c.  it fails to state the original cause

As we all know as we know the universe is created  billion years ago when a small fire ball that exploded.

Big Bang theory is discovered by the George Lemaitre.

It is the explanation "how the universe began."

It states that universe starts from a tiny  point then expanded to grow more larger and it is still expanding.

Big Bang Theory cannot explain Galaxy formation. It cannot solve the problem of universe of origination because it didn't tell where the singular point of Big Bang came.

c. it fails to state the original cause

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When a moving thing slows down, gravity action must be taking place on the object.

Every item is subject to the gravitational pull of the earth, which pulls everything in the atmosphere toward the planet's surface.

Since there is no gravity nor a vacuum in space, the only reason the item is traveling is due to the attraction of the earth's gravitational field.

Therefore, when an item slows down while in motion, gravitational force must be at work. The moon's gravitational pull causes ocean tides, and on Earth, gravity gives weight to physical objects. Additionally, gravity is a key factor in a variety of biological processes, such as gravitropism, which controls plant development, and the fluid movement in multicellular organisms.

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If a certain piece of metal is cooled, it will conduct electricity better, this statement is theory whereas, the amount of electric current that passes through a conductor is directly proportional to the voltage is known as law.

A hypothesis is a statement that may be true or false. A theory is a well-supported explanation of observations or data. A scientific law is a statement that explains the relationship between variables. Hypothesis is a statement that is given before performing an experiment. It can be true or false after we perform an experiment. When a number of experiments can be performed and the hypothesis comes out true then theory is evolved. When the statement is verified after performing large number of experiments, it becomes a law.

So we can conclude that if a certain piece of metal is cooled, it will conduct electricity better, this statement is theory whereas, the amount of electric current that passes through a conductor is directly proportional to the voltage is known as law.

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Net electric field in middle of two charge is equal to 7,318.4 NC⁻.

Electric field at a point by an point electric charge is given by:

E=KQ/r²

where,

E is electric field

K is an constant with value 9×10⁹

Q is point electric charge

r is the distance at which E is desired

for 10.8 nC

electric field at +0.25 m is as

E=+155.2NC⁻

for 51.9nC

electric field at -0.25 m is as

E= - 7473.6NC⁻

therefore net electric field in middle of two charge

=(+155.2- 7473.6)

= -7318.4NC⁻

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By relativistic momentum, the proton speed is 1.93 x 10⁵ m/s.

We need to know about relativistic momentum to solve this problem. The rest energy of the object can be determined by

P = m₀ . v/ √(1 - v²/c²)

where P is relativistic momentum, m₀ is rest mass, c is speed of light (3 x 10⁸ m/s) and v is speed of object.

From the question above, we know that :

mp = 1.6 x 10¯²⁷ kg

me = 9.1 x 10¯³¹ kg

c = 3 x 10⁸ m/s

ve = 0.75c

Find the relativistic momentum of electron

P = me . ve/ √(1 - ve²/c²)

P = 9.1 x 10¯³¹ . 0.75c / √(1 - (0.75c)²/c²)

P = 2.0475 x 10¯²² / 0.66

P = 3.1 x 10¯²² kg.m/s

Find the speed of proton

P = mp . vp/ √(1 - vp²/c²)

3.1 x 10¯²² = 1.6 x 10¯²⁷ . vp / √(1 - vp²/c²)

vp = 193892.05 x √(1 - vp²/c²)

squared

vp² = 3.76 x10¹⁰ -  3.76 x10¹⁰vp²/c²

(1 + 3.76 x10¹⁰/c²) vp² = 3.76 x10¹⁰

(1.0) vp² = 3.76 x10¹⁰

vp = √(3.76 x10¹⁰)

vp = 1.93 x 10⁵ m/s

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The acceleration lasts 0.0077 seconds and is equivalent to 8450 m/s².

The rate at which an object's position changes with respect to time is defined as velocity.

Because it consist of both magnitude and direction, it is a vector quantity. Speed is a scalar quantity that represents the magnitude of velocity. The SI unit of velocity and speed is m/s.

Acceleration is the measure of how quickly a velocity varies over time. It is also a vector quantity. A negative sign of acceleration indicates that the velocity of the body is decreasing with time.  

Given in the question

Initial speed = u = 0 m/s ( as the firework starts from rest)

Final velocity = v = 65 m/s

Distance traveled = 0.25 m

B) Acceleration

Using the third equation of motion,

[tex]v^{2} -u^{2} =2as[/tex]

Put in the value, we get

(65)² - (0)² = 2a(0.250)

0.5a = 4225

a = 8450 m/s²

As a result, fireworks accelerate at 8450 m/s².

A) Time the acceleration lasts

Acceleration is calculated as (Final Velocity - Initial Velocity)/Time.

Put in the values, we get

8450 = 65/time

Time = 65/8450

Time = 0.0077 seconds

Hence, the acceleration lasts for 0.0077 seconds and is 8450 m/s².

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Answer:

X is frictional force

Explanation:

when X is greater than pushing force,the object won't move

The correct answer for the nature of force at "X" is frictional force.

What is friction force?

Friction or frictional force is the force that acts when two surface comes in contact with each other. When a body A is resting upon a body B, The force that helps the body to maintain the equilibrium position is static friction.

Kinetic friction slows down a moving object, when their is relative   motion between two objects. It always acts in apposite direction to the force applied.

It is denoted by [tex]F[/tex].

The formula to calculate static friction is [tex]F = \mu N[/tex]

[tex]\mu_s =[/tex] Co-efficient of static friction

[tex]\mu_k =[/tex] Co-efficient of Kinematic friction.

The Force indicated at "X" is "Kinetic friction", It will slow down the moving object.

When "X" is greater than the moving object, the object will stop moving and will remain at rest.

The Force Indicated at "X" is Frictional force.

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The gravitational force on the box is 580N.

It should be noted that the gravitational force acts perpendicularly downwards and the normal force of the box  is perpendicular to the slanting ramp. This force we are given 538 N.

The gravitational force is the component of this 538 N.

In this case, Cos22° = 538/Y  

Where

y = the gravitational force.

 Cos22° = 538/Y

 Y× Cos22° = 538

 Y = 538/Cos22°

   = 580.25

Therefore, the gravitational force on the box is 580N.

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The magnitude is 167.6cm and the angle (relative to the floor) of the displacement of p is 32.5 degree.

A displacement is a vector in geometry and mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It calculates the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.

A point's ultimate location in relation to its original position, or a displacement, can also be defined as a relative position. The instantaneous velocity of an object is the rate at which the displacement changes as a function of time when studying motions of objects throughout time.

Explanation:

a)

height = 2*r =2*45 cm = 90 cm

y = 1/2 * circumference

   =1/2 * 2*pi*r

   = pi*r

  = pi*45

  = 141.4 cm

displacement  =sqrt ( height^2 + y^2)

   = sqrt (90^2 + 141.4^2)

   = 167.6 cm

Answer: 167.6 cm

b)

angle ,x = atan (height/y)

               = atan (90/141.4)

                = 32.5 degree

Answer: 32.5 degree

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By the velocity, they will travel 6.875 m and the dog catches the man at 2.08s.

We need to know about velocity to solve this problem. Velocity can be determined as the distance traveled divided by time interval. It can be written as

v = s / t

where v is velocity, s is distance and t is the time interval.

From the question above, we know that.

v man = 1.5 m/s

v dog = 3.3 m/s

to = 2.5s

Determine the distance traveled by man when the dog waits

so = vman . to

so = 1.5 x 2.5 = 3.75 m

Find the man's total distance

total distance = distance after dog run + distance when the dog waits

total distance = vman . t + 3.75

We know that the total distance by man's will be caught by the dog, Thus

total distance = vman . t + 3.75

v dog . t = 1.5t + 3.75

3.3t = 1.5t + 3.75

1.8t = 3.75

t = 2.08 s

Find total distance

total distance = vdog . t

total distance = 3.3 x 2.08

total distance = 6.875 m

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Dynamics sound helps differentiate between the sound of a fire truck, an ambulance and an 18-wheeler.

Elements allude to the din or delicateness of music. Elements offer a method for showing articulation in printed music. They help to drive the profound substance of music through volume and force. Elements can likewise be shown at the large-scale level for a piece of music in general. This may be just a single time toward the beginning, or a few times all through in the event that the din changes during various segments. Static elements are melodic directions that advise us to play the music at a specific volume that doesn't change. As such, don't get stronger or calmer, play each note at a similar volume as the final remaining one.

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An elevator is being lifted up an elevator shaft at a constant speed by a steel cable. All frictional effects are negligible. In this situation, forces on the elevator are such that the upward force of the cable is equal to the downward force of gravity.

As per Newton's 2nd regulation F = ma, acceleration needs a force proportional to mass. So when the elevator is accelerating upwards, it has to not handiest oppose gravity however provides greater pressure for the upward acceleration. This calls for an expanded ordinary force

Friction is the pressure resisting the relative motion of strong surfaces, fluid layers, and cloth factors sliding against each other. There are several types of friction: Dry friction is a pressure that opposes the relative lateral movement of two solid surfaces in touch.

The gravitational force is a pressure that draws any gadgets with mass. We call the gravitational pressure attractive as it usually attempts to pull masses collectively, it in no way pushes them apart. In fact, each item, which includes you, is pulling on each other object in the entire universe.

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The directions of the vectors for velocity and acceleration will be [b] the velocity vector points to the right and the acceleration vector points to the left.

The velocity vector is always pointing in the direction that the object is moving. Therefore, from our vantage point, the direction of velocity is to the right.

When an object experiences positive acceleration, the acceleration vector points in the object's motion direction.

When an object experiences a negative acceleration, the acceleration vector is in the opposite direction as the object's velocity. Therefore, from our vantage point, the direction of velocity is to the left.

The rate at which an object's position changes is called its velocity vector. The rate at which an object's velocity changes is called its acceleration vector.

As a result, the vectors for acceleration and velocity point in opposite directions.

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A train slows down as it pulls into a station, if the train is moving from your left to your right, what are the directions of the vectors for velocity and acceleration?

[a] the velocity points to the left and the acceleration vector also points to the left

[b] the velocity vector points to the right and the acceleration vector points to the left

[c] the velocity vector points to the left and the acceleration vector points to the right

[d] the velocity vector points to the right and the acceleration vector also points to the right

the frequency at which gain is maximized for the forced damped harmonic oscillator is ωr .when 0<b<2mω

ωr is the frequency at which gain is maximum.

oscillator is a device that work on the principle of oscillation.

harmonic oscillator - It is a periodic rotation about the main position. That shifts to and fro.

Damped harmonic oscillator - It is a vibrating system for amplitude of vibration decreases over a time.

equation of damped harmonic oscillator.

[tex]\frac{d^{2}x}{dt^{2}} +2k\frac{dx}{dt} + \omega^{2} x = 0[/tex]

ω is the angular frequency

k is resistance coefficient

when 0<b<2mω

ωr is the frequency at which gain is maximum.

the frequency at which gain is maximized for the forced damped harmonic oscillator is ωr

The question is incomplete.

ind the frequency at which gain is maximized for the forced damped harmonic oscillator with equation

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Magnitude of the magnetic fields from largest to smallest is,

[tex]B_{e}\; > \;B_{c}\; > \;B_{b}\; > \;B_{a}\; > \;B_{d}[/tex]

We know that,

[tex]Permeability\;of\;free\;space,\;\mu_{0} = 4 \times \pi \times 10^{-7}\;H/m\\[/tex]

[tex]l=length[/tex]

[tex]I=current[/tex]

(a)

[tex]Radial\;distance,\;r = 2\;cm=0.02\;m[/tex]

[tex]Current,\;I = 3\;A[/tex]

We know that, Magnetic equation,

[tex]B_{a} =\frac{\mu_{0} \times I}{2\times \pi\times r}[/tex]

Substitute the known values in the above magnetic field equation,

[tex]B_{a}=\frac{4 \times \pi \times 10^{-7} \times 3}{2\times \pi\times 0.02}[/tex]

By solving the equation, we get

[tex]B_{a}=3 \times 10^{-5}\;T[/tex]

(b)

[tex]Radius\;of\;the\;coil,\;r = 0.02\;m[/tex]

[tex]Number\;of\;turns,\;N = 10[/tex]

[tex]Current,\;I = 0.3\;A[/tex]

We know that, Magnetic equation,

[tex]B_{b} =\frac{\mu_{0} \times N \times I}{2\times r}[/tex]

Substitute the known values in the above magnetic field equation,

[tex]B_{b}=\frac{4 \times \pi \times 10^{-7} \times 10 \times 0.3}{2 \times 0.02}[/tex]

By solving the equation, we get

[tex]B_{b}=9.425 \times 10^{-5}\;T[/tex]

(C)

[tex]Length\;of\;the\;solenoid,\;l = 2\;m[/tex]

[tex]Number\;of\;turns,\;N = 1000[/tex]

[tex]Current,\;I = 0.3\;A[/tex]

We know that, Magnetic equation,

[tex]B_{c} =\frac{\mu_{0} \times N \times I}{l}[/tex]

Substitute the known values in the above magnetic field equation,

[tex]B_{c}=\frac{4 \times \pi \times 10^{-7} \times 1000 \times 0.3}{2}[/tex]

By solving the equation, we get

[tex]B_{c}=18.85 \times 10^{-5}\;T[/tex]

(d)

[tex]Current\;through\;the\;bar,\;I = 300\;A[/tex]

At the center of the conductor if we consider an Amperian loop of zero radius, no current will be enclosed by this loop.

Hence, At the center of the conductor magnetic field will be zero

[tex]B_{d}=0[/tex]

(e)

[tex]1 mT=1 \times 10^{-3}[/tex]

Therefore,

[tex]B_{e}=1 \times 10^{-3}\;T[/tex]

Therefore, Magnitude of the magnetic fields from largest to smallest is,

[tex]B_{e}\; > \;B_{c}\; > \;B_{b}\; > \;B_{a}\; > \;B_{d}[/tex]

When placed inside a magnetic field, a material's permeability—which is defined as the number of magnetic lines of force that may pass through a specific surface—allows magnetic flux to pass through it.

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The volume of the 4.00 cm length of the, 1.85 mm thick cylinder pump, that comes to thermal equilibrium with the air is approximately 6.24 cm³.

Parameters of the question found in a similar question found online are as follows;

Thickness of the steel cylinder, t = 1.85 mm

Length of steel cylinder that comes to thermal equilibrium with the air, l = 4.00 cm

Given parameters;

Inner diameter of the cylinder, d = 2.50–cm

Length of the cylinder = 50.0–cm

Required; Volume of the steel in the 4.00–cm length

Solution;

1.85 mm = 0.185 cm

Volume of the cylinder, V, is found as follows;

V = π•(D² - d²)/4 × l

Where;

D = The outer diameter of the cylindrical pump

d = The inner diameter

l = Length of the cylinder

Therefore;

D = d + 2•t

Which gives;

D = 2.5 + 2 × 0.185 = 2.87

V = (π•(2.87² - 2.5²)/4) × 4 ≈ 6.24

Therefore;

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At a point halfway between the center and any vertex, the field is stronger.

An equilateral triangle with side L is formed by the bend of a wire carrying a current I.

The magnetic field created by a straight wire is given as:

[tex]B = \frac{ \mu_{0} I}{2 \pi a}[/tex]

The cosines of the complementary angles are identical to the sines of the angles that appear in that equation.

For the distance "a" from the wire to the field point,

We obtain:

[tex]tan{~}30^{\circ} = \frac{a}{L/2}\\a = 0.2887L[/tex]

We have one whole side of the triangle that generates a magnetic field at the center of the triangle is [tex](\frac{ \mu_{0} I(1.732)}{4 \pi a} )[/tex].

Now, the near side of a triangle will be at a geometrically equivalent location and will be half as far from point P(b).

Then the field at P(b) is:

[tex](\frac{ \mu_{0} I(1.732)}{4 \pi a} )= \frac{2 \mu_{0} I (1.732)}{4 \pi a}[/tex]

A P(b) field is created by the two half-sides that are cross-hatched which is:

[tex]2(\frac{2 \mu_{0} I(1.732)}{4 \pi a} )= \frac{4 \mu_{0} I (1.732)}{4 \pi (0.2887L)}=\frac{6 \mu_{0} I}{ \pi L}[/tex]

We already have evidence that the field at P(b) is stronger because the remaining triangle will contribute a little bit more field in the same direction.

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The average acceleration of the ball while it is in contact with the wall is 1634.48 m/s²

Speed of the ball, v = 23.7 m/s

Contact timing of the ball with the wall, t = 0.0145 s

Since,  average acceleration of the ball while it is in contact with the wall is being asked, so we can neglect the rebound speed.

So according to the First Equation of Motion which relates the velocity, acceleration and time i.e.

v = u +at

u = 0 as the initial velocity of the ball is zero

v = at

a = [tex]\frac{v}{t}[/tex]

a = [tex]\frac{23.7}{0.0145}[/tex]

a = 1634.48 m/s²

The average acceleration of the ball while it is in contact with the wall will be 1634.48 m/s²

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(c) The fundamental frequency of one of the organ pipes will go up or increase.

When pressured air is forced into an organ pipe, it echoes at a particular pitch, generating the sound of the pipe organ. Each pipe has been adjusted to a particular pitch on the musical scale.

An outdoor pipe organ is a type of musical instrument used to perform music. It sounds quite serene and produces some calming tones.

The organ pipe produces the sound of the outdoor organ. The wavelength of the sound is also dependent on the length of the pipe. The fundamental frequency of one of the organ pipes will grow as the speed of the sound increases as the ambient air temperature rises.

The correct option is (c).

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Answer:

Explanation:

it should be 3.2 m/s^2

The acceleration is 3.2 m/ s2. Acceleration is change in velocity per time.

Any procedure where the velocity varies is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.

A moving object can occasionally alter its velocity by the same amount every second. The data table above depicts an item altering its velocity by 10 m/s every second, as was described in the paragraph above. Since the velocity is changing by a fixed amount every second, this is known as a constant acceleration.

Therefore, The acceleration is 3.2 m/ s2. Acceleration is change in velocity per time.

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The direction of the bird's velocity can be adjusted so that the wind and the resulting bird velocity will both be in the southerly direction.

(a) The bird should fly at an angle of roughly South 23.58° East if it wants to move directly southward in relation to the earth.

(b) The bird would need around 5.46 hours to fly 500 kilometres from North to South.

The components of the velocity are v(x) and v(y).

The magnitude of the velocity of the bird is 100 km/h

The orientation of the bird corresponds to that of North and South.

The magnitude of the velocity of the wind is 40 km/h

East-west is the direction of the wind.

(a) The component vector of the two velocities are;

The velocity of the bird, v(y) = -100(j)

The velocity of wind, v(x) = 40(i)

If the bird has a component of velocity to accommodate the wind velocity, the direction of its movement will be southerly.

Let θ be the angle of the direction of the bird relative to the negative x-axis, therefore:

-100(j) × cos(θ) = -40·i

θ = cos⁻¹(40/100)

θ ≈ 66.42° in the third quadrat, given that both the y, and x, values are negative.

In the South-West direction, the angle is:

90 - 66.42 ≈ 23.58°

Therefore, to fly directly southward relative to the ground, the bird should fly in the direction of south 23.58° east.

(b) The following is given as the component of the bird's southerly velocity when traveling in the new direction:

v(s) = 100 × sin(θ)

Hence,

Southward velocity,  v(s) = 100 × sin(66.42°)

The time t it takes to travel 500 km, is given as:

d = v(s)t

500 = 100 × sin(66.42°)(t)

t = 5.46 hrs

The bird would need 5.46 hours to fly 500 kilometres from North to South.

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The complete question is mentioned below:

Canada geese migrate essentially along a north–south direction for well over a thousand kilometres in some cases, traveling at speeds up to about 100 km/h. If one goose is flying at 100 km/h relative to the air but a 40-km/h wind is blowing from west to east,

(a) at what angle relative to the north–south direction should this bird head to travel directly southward relative to the ground?

(b) How long will it take the goose to cover a ground distance of 500 km from north to south? (Even on cloudy nights, many birds can navigate by using the earth’s magnetic field to fix the north–south direction.)

When gas particles contact with one another at a fixed temperature and volume, the average kinetic energy of the gas remains constant. Given that the temperature stays constant, this is the case. This characteristic gives us some understanding of the kinetic energy of the particles; for example, if the temperature rises, we may predict that the kinetic energy will follow suit. However, this kind of energy does not change if the temperature stays constant.

A particle or an item that is in motion has a sort of energy called kinetic energy. When work, which entails the transfer of energy, is done on an object by applying a net force, that object acquires kinetic energy.

Mass and speed are the two fundamental variables that influence kinetic energy. Why? Because an object's motion is dependent on both its velocity and its mass, though velocity plays a larger role in motion.

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The ion rocket engine give an acceleration to the space probe of: 0.001 m/s²

To solve this exercise, the formula and procedure to be applied is:

F = m * a

Where:

Information about the problem:

Applying the force formula and isolating the acceleration, we get:

F = m * a

a = F/m

a = 1 N /1000kg

a =  1 kg * m/s² / 1000kg

a = 0.001 m/s²

It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.

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If the table says that the atomic number of the element is 12 and the mass number of the element is 40, then the element has 12 protons and 28 neutrons, therefore the correct answer is option C.

It is the sum of the mass of all the protons as well as the neutrons that are present inside the nucleus.

The addition of protons and neutrons represents the mass number of any element.

The mass number of any element is the sum of the number of protons and the number of neutrons, therefore the correct answer is option C.

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Mr. spoke is travelling with speed v = 9.4c.

Mr. spoke is apparently unknowing of  theory of special relativity by Einstein. The theory states that moving clock tick slower than stationery clock.

Time elapse =∆t = 3 weeks

(In earth stationery frame)

Time ellipse= ∆t' = 1 week

(In the frame of rocket)

∆t' = ∆t'/γ

1/y² = 1 - v²/c²

∆t'²/∆t² =

=1²/3²

=1/9

c= 3×10⁸m/s

on solving above equation we get :

v = 9.4c

He was spreading around at close to the speed of light.

Experience significant time dilatation.

He is travelling with speed  v = 9.4c.

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The radius of curvature of the proton's path while in the field is [tex]66.67[/tex]  × [tex]10^{-2}[/tex].

b) Let R = radius curvature of protons path. Then,

relation b/w B, R, and v is: -

[tex]B = mv/eR\\R=mv/eB[/tex]

[tex]R=\frac{1.6*10^{-27} * 20*10^{6}}{1.6*10^{-19}*0.3 }[/tex]

[tex]R =66.67[/tex]× [tex]10^{-2}[/tex]

Hence, the radius of curvature of the proton's path while in the field is [tex]66.67[/tex] × [tex]10^{-2}[/tex].

The magnetic influence on moving electric charges, electric currents and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is travelling through a magnetic field.  The magnetic field of a permanent magnet pulls on ferromagnetic substances like iron and attracts or repels other magnets. A magnetic field that varies with location will also exert a force on a variety of non-magnetic materials by changing the velocity of those particles' outer electrons. Electric currents, like those utilized in electromagnets, and electric fields that change in time produce magnetic fields that surround magnetized things.

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The frequency that the driver detects after the police car passes him is 2.08 kHz.

The quantity of waves that pass a set location in a predetermined period of time is known as frequency. Therefore, if a wave passes through in half a second, the frequency is 2 per second. The frequency is 100 per hour if it takes 1/100 of an hour. Frequency is typically expressed in hertz units, which were created in honor of German physicist Heinrich Rudolf Hertz in the 19th century. The frequency, abbreviated as Hz, refers to the number of waves that move across a space in a second. An "A" note on a violin string, for instance, vibrates at roughly 440 Hz (440 vibrations per second).

frequency = 1/T

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The initial velocity with which the rock was launched is 41.16 m/s and the maximum height achieved by the rock is 86.4 m.

The three equations of motion are -

v = u + at

S = ut + 1/2 at²

v² - u² = 2aS

Given is a rock launched from ground vertically upwards reaching its highest point after 4.2 s of being launched. Therefore, we can write -

Time taken to achieve maximum height [t] = 4.2 sec

Acceleration [a] = - 9.8 m/s²

Assume that the initial velocity is u.

Therefore - at maximum height S[max],  t = 4.2 s

Now, at maximum height, final velocity (v) will be zero.

From the first equation of motion -

v = u + at

0 = u - gt

u = gt

u = 9.8 x 4.2

u = 41.16 m/s

The initial velocity of rock was 41.16 m/s.

The maximum height achieved by the rock -

S[max] = ut + 1/2 at²

S[max] = 41.16 x 4.2 - 0.5 x 9.8 x 4.2 x 4.2 = 172.87 - 86.44 = 86.4 m

Therefore, the initial velocity with which the rock was launched is 41.16 m/s and the maximum height achieved by the rock is 86.4 m.

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