How much work is done on a 6.4N box of books that you move horizontally across a 6.1 meter room?​

Explanation:

To find the y-component of a vector that is 14.4 m long and points in a 133 degree direction, you can use the trigonometric functions sine and cosine.

The y-component of a vector is given by the product of the vector's length and the sine of the angle between the vector and the positive x-axis. The x-component of a vector is given by the product of the vector's length and the cosine of the angle between the vector and the positive x-axis.

You can find the y-component of the vector by using the formula:

y-component = vector length * sine(angle)

In this case, the vector length is 14.4 m, and the angle between the vector and the positive x-axis is 133 degrees. You can find the y-component of the vector by plugging these values into the formula:

y-component = 14.4 m * sine(133 degrees)

You can use a calculator or look up the value of sine(133 degrees) in a table to find the y-component of the vector. You will find that the y-component of the vector is approximately -11.9 m.

Note that the y-component of the vector is negative because the vector points in a direction that is below the positive x-axis. The x-component of the vector would be positive because the vector points in a direction that is to the right of the y-axis.

Use the trigonometric functions sine and cosine to determine the y-component of a vector that is 14.4 m long and points in a 133 degree direction.

A vector's y-component is calculated by multiplying its length by the sine of the angle it makes with the positive x-axis. A vector's x-component is calculated by multiplying its length by the cosine of the angle it makes with the positive x-axis.

Utilizing the following formula, you can get the vector's y-component: y-component = sine * vector length (angle).

The vector length in this instance is 14.4 m, and the angle it makes with the positive x-axis is 133 degrees. the location of the y-component.

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The maximum work is developed when the pressure ratio is the same across each stage as Pi/P2 =  P1/Pi

Describe work.

When an object is moved over a distance by an external force, at least some of that force must be applied in the direction of the displacement. That is called work. Work is a measure of energy transfer.

The definition of energy is the capacity for work. The work produced is consistent. There are many different types of energy, including kinetic and potential energy.

The turbine work ,w =(h 1−h a)(h b −h 2 )

                                   =cp [(T 1−Ta)+(T b−T 2 )]

As the temperature at the inlet at each stage is same: T 1=T b

So ​

turbine work ,w =  cp [(T 1−Ta)+(T b−T 2 )]

                           =  cp [2T1-Ta -T2]

                           =  cp*T1[2- Ta/at1 - T2/T1]

Ta/T1 = (Pi/P1)^x

T2/T1 = (P2/Pi)^x

and x =(k-1)/k

So , w =c p*T 1 [2−( P1/Pi)^ x−( Pi/P2)^x ]

In case of maximum work done , dw/di = 0

Substituting it in above equation gives:

P1*P2 = (Pi)^2x

Pi/P2 =  P1/Pi

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A block of mass 0.40 kg and density 2900 kg/m3 is completely submerged under the water in static equilibrium on top of a spring (k = 50.0 N/m) that is fixed to the bottom of the container, the spring is compressed by 0.051 m.

To determine the amount that the spring is compressed, you will need to consider the mass of the block, the density of the block and the water, and the spring constant of the spring.

The weight of the block is equal to the mass of the block times the acceleration due to gravity.

The equation for the weight of the block can be written as:

W = m * g

where W is the weight of the block, m is the mass of the block (0.40 kg), and g is the acceleration due to gravity (9.8 m/s^2).

Plugging in the values, you get:

W = 0.40 kg * 9.8 m/s^2

W = 3.92 N

The buoyant force acting on the block is equal to the weight of the water displaced by the block. The weight of the water displaced by the block is equal to the volume of the block times the density of the water times the acceleration due to gravity.

The equation for the buoyant force can be written as:

F_b = V * rho_w * g

where F_b is the buoyant force, V is the volume of the block, rho_w is the density of the water (1000 kg/m^3), and g is the acceleration due to gravity (9.8 m/s^2).

The volume of the block can be calculated using the density of the block and the mass of the block.

The equation for the volume of the block can be written as:

V = m/rho

where V is the volume of the block, m is the mass of the block (0.40 kg), and rho is the density of the block (2900 kg/m^3).

Plugging in the values, you get:

V = 0.40 kg / 2900 kg/m^3

V = 0.0014 m^3

Plugging this value into the equation for the buoyant force, you get:

F_b = 0.0014 m^3 * 1000 kg/m^3 * 9.8 m/s^2

F_b = 1.37 N

The net force acting on the block is equal to the weight of the block minus the buoyant force.

The equation for the net force can be written as:

F_net = W - F_b

where F_net is the net force, W is the weight of the block, and F_b is the buoyant force.

Plugging in the values, you get:

F_net = 3.92 N - 1.37 N

F_net = 2.55 N

The spring force is equal to the spring constant times the amount that the spring is compressed.

The equation for the spring force can be written as:

F_s = k * x

where F_s is the spring force, k is the spring constant (50.0 N/m), and x is the amount that the spring is compressed.

Solving for x, you get:

x = F_s / k

Plugging in the values, you get:

x = 2.55 N / 50.0 N/m

x = 0.051 m

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The required  speed of the center of mass of the two-car system is 10 m/s.

Option(2) is corret.

The reason is simple. Velocity is the percentage of time an object moves along a path, and Velocity is the speed and direction of an object's movement.

The mathematical calculation of velocity is relatively simple, the average velocity of an object is calculated by dividing the distance traveled by the time it took the object to travel that distance. Velocity, on the other hand, is mathematically complex and can be calculated in different ways depending on what information is available about the object's motion. In its simplest form, the average velocity is calculated by dividing the change in position (Δr) by the change in time (Δt).

Let the mass of cars which is same is M,

Speed (V1) = 30 m/s

Speed (V2) = -10 m/s

Then,

Speed of center of mass = MV1 + MV2/2M

Speed of center of mass = M(30) + M(-10)/2M

Speed of center of mass = 30M - 10M/2M

Speed of center of mass = 20M/2m

Speed of center of mass = 10 m/s

Thus, Speed of center of mass is 10 m/s

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Answer:

The average deceleration of the car can be calculated using the formula for deceleration, which is given by the change in velocity divided by the time over which the change occurs. In this case, the initial velocity of the car is 200 m/s, the final velocity is 0 m/s, and the time over which the change occurs is 2 seconds. Therefore, the average deceleration can be calculated as follows:

Deceleration = (0 m/s - 200 m/s) / 2 s = -100 m/s^2

The negative sign indicates that the deceleration is in the opposite direction to the initial velocity of the car, which is what we would expect in this case, since the car is slowing down. Therefore, the average deceleration of the car is -100 m/s^2.

C. Are B, C, and A in a series? Three layouts are shown, two in parallel and one in series. The resistance of each resistor is same. r. sort in declining order the analogous resistances of the layouts.

In resistors, electrical energy is transformed into heat that is subsequently dissipated. With negative and positive charges kept apart, capacitors are frequently employed to filter frequencies. Alternative current can be passed through capacitors while direct current is blocked.

Electrical resistance is provided by a resistor, a two-terminal electrical component. Resistors are mainly used to split voltages, impede transmission signals, reduce current flow, and bias active components in electronic circuits.

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The applied force must be larger than the frictional force for a body to move successfully.

Between two surfaces that are sliding or attempting to slide over one another, there is a force called friction. For instance, friction makes it challenging to push a book down the floor. Friction always moves an object in a direction that is counter to the direction that it is traveling or attempting to move.

When a body is pushed, an exact quantity of frictional force is created, up until the point where Fs max = coefficient of friction * normal force.

After that, when fs max exceeds the frictional force, dynamic friction enters the picture, which is what causes the body to move.

The body begins to move after a force is applied that is more than the minimal need, or what we refer to as the Threshold (f applied > fs max).

In the case of a frictionless surface, the applied force will be perpendicular to the gravitational force that is being taken into account. Even the slightest acceleration must cause the body to move.

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Answer:

Explanation:

Vertical acceleration.

A nova or supernova may be the most catastrophic occurrence in all of nature.

A negatively charged subatomic particle called an electron can either be free or attached to an atom (not bound). One of the three main types of particles in an atom is an electron that is attached to it; the other two are protons and neutrons.

For creating cross-platform desktop apps using HTML, CSS, and JavaScript, GitHub developed the open source library called Electron. Chromium and Node are combined to create Electron, which does this. Apps may be produced for Mac, Windows, and Linux and combined with JavaScript into a single runtime.

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To find the minimum amount of ice needed to cool the tea, you can use the formula:

Q = mcΔT + mL

where Q is the heat energy required, m is the mass of the ice, c is the specific heat capacity of ice, ΔT is the temperature change, and L is the latent heat of fusion.

The specific heat capacity of ice is 2010 J/kg°C. The latent heat of fusion of ice is 3.34 x 10^5 J/kg.

First, find the heat energy needed to cool the tea from 91.98°C to 6.19°C:

Q = 2.70 kg * 4190 J/kg°C * (91.98°C - 6.19°C) = 2.70 kg * 4190 J/kg°C * 85.79°C = 92959.58 J

Then, find the heat energy needed to melt the ice:

Q = mL = m * 3.34 x 10^5 J/kg = m * 3.34 x 10^5 J/kg

Then, add the heat energy needed to cool the tea to the heat energy needed to melt the ice:

Q = 92959.58 J + mL = 92959.58 J + 3.34 x 10^5 J/kg * m

Finally, rearrange the equation to solve for m:

m = (Q - 92959.58 J) / (3.34 x 10^5 J/kg)

Plugging in the given values, you get:

m = (92959.58 J - 92959.58 J) / (3.34 x 10^5 J/kg) = 0 kg

So the minimum amount of ice needed to cool the tea is 0 kg. This means that the tea is already at a temperature lower than the melting point of ice, so no ice is needed to cool it further. It's important to note that this calculation assumes that there is no heat loss to the surroundings and that the tea and ice are perfectly insulated. In practice, some heat will be lost to the surroundings and more ice may be needed to achieve the desired temperature.

The resistance of the wire, given that it is connected to a 9.0 V power pack and an ammeter is 36 ohms

From Ohm's law, we understood that the voltage, current and resistance are related according to the following formula:

Voltage (V) = Current (I) × resistance (R)

V = IR

Using the above formula, we can obtain the resistance of the wire as follow:

Voltage (V) = Current (I) × resistance (R)

9 = 0.25 × resistance

Divide both sides by

Resistance = 9 / 0.25

Resistance = 36 ohms

Thus, we can conclude that the resistance of the wire is 36 ohms

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The super keys of the relationship if a relation R(A, B, C, D) with four attributes A, B, C, and D is 8.

The quality of a feature is referred to as an attribute. The theory of attributes is concerned with the calculation of qualitative forms of qualities using quantitative measures. As a result, the characteristic requires slightly different types of statistical analyses than the variables do.

The given data,

Given three functional dependencies,

AB → C

BC → D

C → E

Finding the key of the relation, Compute closure of attribute,

{AB}⁺ = {A, B, C, D, E} {BC}⁺ = {B, C, D, E} {C}⁺ = {CE}

Only one candidate key is possible for a given relation = AB

Super keys of the relation = 2 (Total number of attributes in relations - Total number of attributes in each key).

Super keys of the relation = 2⁽⁵⁻²⁾

Super keys of the relation = 2³ = 8 keys

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Answer: 13 m/s.

Explanation: To solve this problem, we need to use the equation for motion with constant acceleration:

d = v₀t + 1/2 at²

where d is the distance traveled, v₀ is the initial velocity, t is the time it takes to travel that distance, and a is the acceleration.

Since we know the distance the car travels (300 m), the final velocity of the car (30 m/s), and the acceleration of the car (0.75 m/s²), we can solve for the initial velocity. We just need to rearrange the equation to solve for v₀:

v₀ = (d - 1/2 at²) / t

In this case, we can plug in the known values to find the initial velocity:

v₀ = (300 - 1/2 * 0.75 * t²) / t

Since the final velocity of the car is 30 m/s and the acceleration is 0.75 m/s², we can use the equation for motion with constant acceleration to find the time it takes for the car to travel 300 m:

v = v₀ + at

30 = v₀ + 0.75t

Rearranging to solve for t, we get:

t = (30 - v₀) / 0.75

Substituting this value for t in the equation for the initial velocity, we get:

v₀ = (300 - 1/2 * 0.75 * ((30 - v₀) / 0.75)²) / ((30 - v₀) / 0.75)

This simplifies to:

v₀ = (300 - 1/2 * 0.75 * (900 - 2v₀) / 0.75) / (30 - v₀)

which simplifies further to:

v₀ = (300 - 675 + v₀) / (30 - v₀)

Solving for v₀, we get:

v₀ = -375 / -29

which simplifies to:

v₀ = 13 m/s

Therefore, the initial velocity of the car is 13 m/s.

Answer:

The fuse in a plug is a safety device designed to protect the lead rather than the appliance. It is a deliberate weak link in a circuit which will 'blow' if an electrical appliance or extension lead draws too much current due to either an overload or a fault.

The correct statement about the direction of  transfer of energy  in an isolated system is b) In an isolated system, energy always transfers from a warmer region to a cooler region .So, correct option is b.

An isolated system is a thermodynamic framework that can't trade either energy or matter beyond the framework. There are two manners by which this might happen: The framework might be so far off from another framework that it can't associate with them. The framework might be encased to such an extent that neither energy nor mass might enter or exit.

When temperature remains constant then energy transfer takes place between different components of system will be possible.Since temperature is different ,energy flow is favored from the warmer region to colder region because of difference in temperature.

Hence, correct option is b.

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(Complete question) is:

Which one of the statements below describes the direction of thermal energy transfer in an isolated system?

a)In an isolated system, for energy transfer to take place the entire system must remain at a constant temperature.

b)In an isolated system, energy always transfers from a warmer region to a cooler region

c)In an isolated system, energy always transfers from cooler region to a warmer region

d)In an isolated system, no transfer of energy between regions of the system can take place.

e)In an isolated system, energy cannot be transferred from a hotter region to a colder region.

When there is compression of 3.63 cm in the spring , block will have maximum velocity. there after its speed will start decreasing.

What is potential energy of a spring?

When spring is stretched, it undergoes displacement. It comes to its equilibrium position when force is removed. So, it exerts an equal and opposite force When it is stretched. Work is done by this force that is stored in the form of potential energy.

Since potential energy = force × displacement

and, force = spring constant × displacement

So, potential energy = spring constant × (displacement)²

According to the given question:

a ) work done by gravitational force

= mg sinθ ( d + .21)

Potential energy stored in compressed spring

= 1/2 k x²

= .5 x 431 x ( .21 )²

= 9.5

According to conservation of energy

mg sinθ ( d + .21)  = 9.5

3.2 x 9.8 x sin 30( d + .21 ) = 9.5

d = 40 cm

b )

As long as mg sin30 is greater than kx ( restoring force ) , there will be acceleration in the block.

mg sin30 = kx

3.2 x 9.8 x .5 = 431 x

x =  3.63 cm

When there is compression of 3.63 cm in the spring , block will have maximum velocity. there after its speed will start decreasing.

Complete question:

A 3.20 kg block starts at rest and slides a distance d down a frictionless β = 30.0 ◦ incline, where it runs into a spring with spring constant k = 431 N/m. The block slides an additional 21.0 cm before it is brought to rest momentarily by compressing the spring. (a) What is the value of d? (b) Where is the speed of the block at the maximum value?

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The time interval during which the speed of the wheel is increasing is 4 s.

Angular acceleration is the term used to describe the temporal pace at which angular velocity varies. Radians per square second is used as the measurement unit.

At time t = 0, the angular velocity is ω₁ = - 6.00 rad/s.

At time t = 10.0 s, the angular velocity is ω₂ = +4.00 rad/s.

Angular acceleration of the wheel can be written as= change in angular velocity /time interval

= ( 4.00 - (-6.00))/10 rad/s²

= 1.0 rad/s²

Hence, angular velocity becomes zero at time = ( 0 - ( -6))/1.0 s = 6 s.

So, during t = 0 to t = 6s, the clockwise angular  velocity of the wheel decreases from 6.00 rad/s to 0.00 rad/s and  during t = 6s to t = 10s , the counterclockwise angular  velocity of the wheel increases from 0.00 rad/s to +4.00 rad/s.

Hence,  the time interval during which the speed of the wheel is increasing is = 10 s - 6 s = 4 s.

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As per the given resistances, the equivalent resistance between points a and b will be equal to  14.43 Ω.

When an electric current passes through a lightbulb or any other conductor, the conductor presents some resistance to the current.

This resistance is referred to as resistance value and is represented by the letter R. Since every substance has some electrical resistance, when current flows through a conductor, heat is released.

As per the given figure in the question,

Firstly, calculate the total resistance between points d and c,

R₂ = 35 + 56

R₂ = 91 Ω

Now,

R₁ = 22 Ω

R₂ = 91 Ω and,

R₃ = 78 Ω

All are connected in parallel,

[tex]\frac{1}{R_a_b}[/tex] = 1/22 + 1/91 + 1/78

= 5408/78078

[tex]R_a_b[/tex] = 14.43 Ω.

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Over an AC generator, a series connection between a capacitor and a resistor is made. The voltage across the capacitor is 90 degrees behind the current.

Voltage is the pressure from the power source of an electrical circuit that drives charged electrons (current) through a conducting loop, allowing them to perform tasks like lighting a lamp. Briefly stated, voltage equals pressure and is measured in volts (V).

The energy per unit charge is known as voltage, also known as electromotive force. Voltage is the difference in electric potential between two locations, to put it another way. The pace at which an electric charge flows is known as current.

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The highest possible The value of a graph, also known as the global maximum, is the location where the graph's y value achieves its absolute maximum.

To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f”(x). The second derivative will have a minimal value if it is positive.

The two blocks are thought to be in a balance. If we force P to go to £2.69, then there is no maximum value and one piece equals zero. Zero is less than that, hence the system ought to be in equilibrium. If the force p is in at £2.69, then it must be of equal brands. When everyone is balanced.

Therefore, The maximum value for the entire function is at this point. The location on a graph where the y-coordinate has the lowest value is known as the minimal value.

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The fringe separation of the double-slit interference is 0.884 mm.

When two coherent light waves from separate sources collide, the energy distribution caused by the first wave is altered by the second. The term "interference of light" refers to this alteration in the distribution of light energy brought on by the superposition of two light waves.

Wavelength of light: λ = 680 nm = 680 × 10⁻⁹ m.

Separation between the two slits: d = 0.1 mm = 0.1 × 10⁻³ m.

Screen distance: D = 1.3 m.

Hence, the fringe separation: x = λD/d

= ( 680 × 10⁻⁹)×(1.3 )/(0.1 × 10⁻³ ) m

= 0.000884 m

= 0.884 mm.

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The magnitude of the force that must be applied to the wedge must be equal to the weight of the block, or force = mg.

If the block is to remain at a constant height above the tabletop, then the net force acting on it must be zero. The only force acting on the block is the normal force, which is the force exerted by the wedge on the block. Since the block is not accelerating, the normal force must be equal and opposite to the gravitational force acting on the block. This means that the magnitude of the normal force must be equal to the weight of the block, which is mg, where g is the acceleration due to gravity.

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The stones needed to be dropped from the same height. The light stone is moving quicker than the hefty stone just as it touches the ground. The light stone is taller when it is first placed than the heavy stone is.

Energy is the ability to carry out work. Potential, kinetic, thermal, electrical, chemical, nuclear, and other forms may all exist for it.

There are numerous types of energy. Examples of these include: electromagnetic energy, chemical energy, nuclear or atomic energy, mechanical energy, gravitational energy, electrical energy, sound energy, and so on. Each form can be changed or transformed into the others.

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Answer: Temperature

Explanation:

Answer:

Answer:

let the first point be a second be b third be c fourth be d and last point be e.

The point a and d are incorrect. because tye plotting of the is incorrect

Answer:

The energy of the system and total momentum are both conserved in an elastic head-on collision. The atomic nucleus receives 1.87 percent of the neutron's kinetic energy and final kinetic energy is 12.3×10-13J.

Explanation:

In elastic head-on collision, the energy of the system and total momentum is conserved.

For the neutron,

m - mass, - initial velocity,  - final velocity

For the atom,

M- mass , - initial velocity, - final velocity

Conserved momentum on the head-on collision

mv_i=mv_f+MV_f

v_i-v_f=MmV_f

v_i-v_f=14.9V_f.........(I)

The kinetic energy

v_i^2-v_f^2=14.9V_f^2............(II)

From equation (I) and (II)

(v_i-v_f)/(v_i^2-v_f^2 )=(12v_f^2)/(12v_f^2 )

v_i+v_f=V_f.........(III)

Solve equation (I) and (III) for  

v_i=7.9v_f

Now, the fraction of the neutron's kinetic energy transferred to the atomic nucleus,

(1/2 MV_f^2)/(1/2 mv_i^2 )=14.9/7.95=1.87

K2=1.87×6.58×10-13J=12.3×10-13J

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Answer:

D

Explanation:

Direction of motion is positive right side

P = mv

P = m (final - initial)

P = 2 ( -1 - 3)

P = 8 Ns

(negative sign ignored)

I hope my answer helps you.

The impulse on the wall with a mass of the ball is 2 kg and the initial speed of wass 3 m/s and the final velocity is 1 m/s is 8 Ns. Hence, option D is correct.

Impulse equals the product of net force and changes in time. Impulse is also equal to the change in momentum. It is also defined as the force applied to an object with a short duration of time. The unit of impulse is Newton. seconds(Ns).

From the given,

mass of the ball (m) = 2kg

The initial speed of the ball (u) = 3m/s

the final speed of the ball (v) = -1 m/s.

Impulse (I) = Momentum (p)

Momentum (p) = mΔv

                         = m(v-u)

                         = 2(-1-3)

                         = 2(-4)

                         = -8.

Thus, the impulse on the wall is 8Ns.

Hence, the correct option is D.

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The  unit of ETA in terms of the basic units of the SI system is:

ETA = [kg] * [s]⁻¹* [m]⁻¹= kg * s / m

The dimension of the coefficient of viscosity (ETA) can be determined by using the dimensions of the other variables in the equation:

F = ETA * A * (dv/dx)

The dimension of force (F) is [M] * [L] * [T]⁻², the dimension of surface area (A) is [L]⁻², and the dimension of velocity gradient (dv/dx) is [L] * [T]⁻¹.

Since the equation must be dimensionally consistent, we can set up the following equation:

[M] * [L] * [T]⁻²= ETA * [L]² * [L] * [T]⁻¹

Solving for the dimension of ETA, we get:

ETA = [M] * [T]⁻¹ * [L]⁻¹

Therefore, the basic unit of mass in the International System of Units (SI) is the kilogram (kg), the basic unit of time is the second (s), and the basic unit of length is the meter (m). Therefore, the unit of ETA in terms of the basic units of the SI system is:

ETA = [kg] * [s]⁻¹* [m]⁻¹= kg * s / m

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As there is only one force acting on the ball i.e. gravitational force, the acceleration will be constant and downward. Also because ball moves in the direction of the acceleration, the velocity increases.

Acceleration - constant; velocity - increasing.

What is Acceleration?

Acceleration is the rate of change of velocity of an object over time. It can be positive, negative, or zero. Positive acceleration is when an object speeds up, negative acceleration is when an object slows down, and zero acceleration is when an object's velocity remains constant.

What is velocity?

Velocity is a measure of the speed and direction of an object's motion. It is typically measured in meters per second (m/s) or kilometers per hour (km/h). Velocity can also be expressed in other units, such as miles per hour (mph) or feet per second (ft/s). Velocity is related to a object's acceleration, as an object's acceleration is the rate of change in its velocity over time.

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Answer:

To determine the height to which the ball rises before it reaches its peak, we need to know the initial velocity of the ball and the acceleration due to gravity. Let's assume the initial velocity of the ball is v and the acceleration due to gravity is g.

The time it takes for the ball to reach its peak is one-half the total hang-time, or 1/2 * 6.25 s = 3.125 s.

The height to which the ball rises can be calculated using the formula:

height = v * t - (1/2) * g * t^2

Substituting in the values we know, we get:

height = v * 3.125 s - (1/2) * g * (3.125 s)^2

To solve for the height, we need to know the value of v and g. Without more information, it is not possible to determine the height to which the ball rises before it reaches its peak.

Explanation:

Answer:

Approximately [tex]47.9\; {\rm m}[/tex] (assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and that air resistance on the baseball is negligible.)

Explanation:

If the air resistance on the baseball is negligible, the baseball will reach maximum height at exactly [tex](1/2)[/tex] the time it is in the air. In this example, that will be [tex]t = (6.25\; {\rm s}) / (2) = 3.125\; {\rm s}[/tex].

When the baseball is at maximum height, the velocity of the baseball will be [tex]0[/tex]. Let [tex]v_{f}[/tex] denote the velocity of the baseball after a period of [tex]t[/tex]. After [tex]t = 3.125\; {\rm s}[/tex], the baseball would reach maximum height with a velocity of [tex]v_{f} = 0\; {\rm m\cdot s^{-1}}[/tex].

Since air resistance is negligible, the acceleration on the baseball will be constantly [tex]a = (-g) = (-9.81\; {\rm m\cdot s^{-2}})[/tex].

Let [tex]v_{i}[/tex] denote the initial velocity of this baseball. The SUVAT equation [tex]v_{f} = v_{i} + a\, t[/tex] relates these quantities. Rearrange this equation and solve for initial velocity [tex]v_{i}[/tex]:

[tex]\begin{aligned}v_{i} &= v_{f} - a\, t \\ &= (0\; {\rm m\cdot s^{-1}}) - (-9.81\; {\rm m\cdot s^{-2}})\, (3.125\; {\rm s}) \\ &\approx 30.656\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

The displacement of an object is the change in the position. Let [tex]x[/tex] denote the displacement of the baseball when its velocity changed from [tex]v_{i} = 0\; {\rm m\cdot s^{-1}}[/tex] (at starting point) to [tex]v_{t} \approx 30.656\; {\rm m\cdot s^{-1}}[/tex] (at max height) in [tex]t = 3.125\; {\rm s}[/tex]. Apply the equation [tex]x = (1/2)\, (v_{i} + v_{t}) \, t[/tex] to find the displacement of this baseball:

[tex]\begin{aligned}x &= \frac{1}{2}\, (v_{i} + v_{t})\, t \\ &\approx \frac{1}{2}\, (0\; {\rm m\cdot s^{-1}} + 30.565\; {\rm m\cdot s^{-1}})\, (3.125\; {\rm s}) \\ &\approx 47.9\; {\rm m}\end{aligned}[/tex].

In other words, the position of the baseball changed by approximately [tex]47.9\; {\rm m}[/tex] from the starting point to the position where the baseball reached maximum height. Hence, the maximum height of this baseball would be approximately [tex]47.9\; {\rm m}\![/tex].