a system releases 425 kj og heat and does 307 kj of work on the surroundings in the process. what is the change in the internal energy of the system

As the angle of bank rises, a turn coordinator's displacement during a coordinated turn will also rise.

Turn coordinators show information about the speed and quality of the turn as well as the coordination of the turn. Turn and slip indicators solely display turn rate. The turn and bank indication was created. The relative strength of gravity and the inertia brought on by a turn are measured by this ball. The ball will move to the left while the toy airplane makes a turn to the right. What directly displays on the turn coordinator's small aircraft? both the roll and turn rates. A little airplane symbol that rolls (rotates) right or left depending on the bank angle and the rate of turn is used to indicate the turn coordinator's rate of turn.

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The terrestrial planets receive more heat from the Sun and have a lower gravitational pull than the Jovian planets, which receive less heat from the Sun and have a much higher gravitational pull.

Because they are large and composed mostly of gas they are sometimes called gas giants. Small amounts of rocky material are found only deep within the core of Jupiter's planet. In the solar system, Jupiter planet is farther from the Sun than the terrestrial planets and is therefore cooler.

Terrestrial planets formed from rocky and metallic planetesimals but were ultimately too small to capture the large amounts of hydrogen and helium gases abundant in the solar nebula. But Jupiter's planet formed far from the Sun where ice and rock were abundant.

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The distance between the second maximum of laser 1 and the third minimum of laser 2, is 0.36 m.

x1 = nλL / d

n=second maxima of laser 1

  = 2 * (d/20) *5.40 /d

  = 0.54 m

X2= (n+1/2)λL/d

n= 2= third minima of laser 2

  = 2.5 *(d/15)* 5.40 /d

  = 0.9m

distance del(y)max-min between second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum =

0.9 -0.54 = 0.36 m

A laser is a device that produces light by optically amplifying electromagnetic energy through stimulated emission. The term "laser" stands for "light amplification by stimulated emission of radiation" (abbreviated "laser"). The first laser was created in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical research by Charles Hard Townes and Arthur Leonard Schawlow.

Because it emits coherent light, a laser is unique among other light sources. Laser cutting and lithography are made possible by spatial coherence, which makes it possible to focus a laser on a small area.

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The relationship between time of flight t₁ and t₂ is t₂² = 20t₁ +  4.9t₁² = t₂²

The time it takes for the two cannon balls to land or the time of flight is determined using the equation below:

h = ut + ¹/₂gt²

where;

For ball 1:

h = 20t₁ + ¹/₂ * 9.8 * t₁²

For ball 2:

h = 0 * (t₂) + ¹/₂* 9.8 * t₂²

Equating the two values of h:

20t₁ + ¹/₂ * 9.8 * t₁² = 0 * (t₂) + ¹/₂ * 9.8 * t₂²

20t₁ +  4.9t₁² = t₂²

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The combined speed after the inelastic collision is equal to 0.75 v.

An inelastic collision can be described as a type of collision that occurs between two objects in which some energy is lost. In the case of inelastic collision, momentum remains conserved but the kinetic energy will not be conserved.

Given, the mass of cart A, m₁ = 3 m

The mass of the cart B, m₂= m

The initial speed of cart A, u₁ = v

The initial speed of cart B, u₂ = 0

After the inelastic collision the momentum will remain conserved:

m₁.u₁ + m₂u₂ = m₁.v₁ + m₂ v₂

3m × v + m ×0 = (3m + m)× V

V = 3mv/4m

V = 0.75 v

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Since potential energy is inversely proportional to height times mass, an automobile that is twice as large as another will have twice as much potential energy as that vehicle for a given height.

A doubling in height will lead to a doubling in gravitational potential energy since an object's gravitational potential energy is directly proportionate to its height above the zero point. The gravitational potential energy will triple with a tripling of height.

The car's position at the top of the hill's potential energy equals kinetic energy is being created. where "g" is the gravitational constant and equals 9.8 m/s2.

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Answer:

power

power is the rate of doing work. It is equivalent to an amount of energy consumed per unit time. In the SI system, the unit of power is the joule per second (J/s).

If the receiver has a totally absorbing panel measuring 20.0 cm by 35.0 cm oriented with its plane perpendicular to the direction the waves travel, the average force these waves exert on the pane is 1.44X10-18N

Given that length of panel (l)  = 35cm = 0.35m

Breadth of panel (b) = 20cm = 0.2m

Force exerted on the plane (F) =Prad x area

where Prad = pressure of radiation wave and a = area of the pane

To find pressure we know that Prad = I/c where I = intensity of radiation and c = speed of light = 3x10^8m/s

Given that power of wave (P) = 25KW

Diameter of satellite (d) = 575km

I = Power/ 4πd^2 = 25x10^3/4x3.14x(575x10^3)^2 = 6.2x10-9

Prad = 6.2x10-9 /3x10^8 = 2.06 x 10-17

Force (F) = 2.06x10-17x 0.2x0.35=1.44x10-18N

Hence the force exerted on the pane by the waves  = 1.44x10-18N

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For complete question: A satellite 575 km above the earth's surface transmits sinusoidal electromagnetic waves of frequency 92.4 MHz uniformly in all directions, with a power of 25.0 kW. Find If the receiver has a totally absorbing panel measuring 15.0 cm by 40.0 cm oriented with its plane perpendicular to the direction the waves travel, what average force do these waves exert on the panel? Is this force large enough to cause significant effects?

When traveling at the specified speed and wavelength, a wave has a frequency of 13Hz.

The distance that the shapes of waves repeat is known as the wavelength. It is a periodic wave's spatial period.

Expression derived from the relationship between wavelength, frequency, and speed; = v /f

Where v is speed or velocity and f is frequency, is the wavelength.

Wavelength of wave λ = 1m

Speed of wave v =13m/s

Frequency f = ?

We substitute our values into above expression.

λ = v ÷ f

1m = 13m/s ÷ f

f = 13m/s ÷  1

f = 13Hz

As a result, the wave's frequency in hertz is 13Hz when it travels at the given speed and wavelength.

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The wavelength of light is 432 nm in a vacuum.

A plate is a particular type of dish. A dish is usually something that meal is eaten or served from. A plate has a tendency to refer in particular to a flat dish that is suitable for holding meals that don't have a high liquid content material. the opposite common sort of dish is a bowl.

There are 3 forms of plate tectonic limitations: divergent, convergent, and transform plate limitations. This picture suggests the three predominant sorts of plate obstacles divergent, convergent, and transform.

A plate is an extensive, especially flat vessel on which food may be served. A plate also can be used for ceremonial or decorative functions. maximum plates are round, but they may be in any form.

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The collision is perfectly elastic.

A collision is considered elastic if it does not result in a net decrease in the system's kinetic energy. In an elastic collision, both momentum and kinetic energy are conserved.

Kinetic Energy(K.E.)=[tex]\frac{1}{2} mv^{2}[/tex]

Let [tex]K.E_i[/tex] and [tex]K.E_f[/tex] be the initial and final kinetic energy.

From the figure, we have

[tex]K.E_i[/tex] = [tex]\frac{1}{2}[/tex]×4×[tex](1.8)^2[/tex] +  [tex]\frac{1}{2}[/tex]×6×[tex](0.2)^2[/tex]

[tex]K.E_i[/tex] = 6.48+0.12

[tex]K.E_i[/tex] =6.6

and

[tex]K.E_f[/tex] = [tex]\frac{1}{2}[/tex]×4×[tex](0.6)^2[/tex] +  [tex]\frac{1}{2}[/tex]×6×[tex](1.4)^2[/tex]

[tex]K.E_f[/tex] = 0.72+5.88

[tex]K.E_f[/tex] =6.6

Since the initial and final kinetic energy is equal there is perfectly elastic.

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Complete Question:

In the figure, determine the character of the collision. the masses of the blocks, and the velocities before and after are given. the collision is

213.65 atm is the pressure inside the tank if left outside in the sun in the temperature is 37°C.

Gay-Lussac's law states that " the pressure exerted by a gas (of a given mass and kept at a constant volume) varies directly with the absolute temperature of the gas".

According to the law, we have,

[tex]\frac{p_2}{T_2} = \frac{p_1}{T_1}[/tex]

Where,

[tex]p_2[/tex] is final pressure

[tex]p_1[/tex] is initial pressure

[tex]T_2[/tex] is final temperature

[tex]T_1[/tex] is initial temperature

Initial temperature: T₁ = 23° C =273 + 23 K = 296 K.

Initial pressure: p₁ = 204 atm.

Final temperature: T₂ = 37°C = 273 + 37 K = 310 K.

Final pressure: p₂ = ?

Substituting the values we get,

[tex]\frac{p_2}{T_2} = \frac{p_1}{T_1}[/tex]

[tex]p_2[/tex] = [tex]\frac{(p_1)(T_2)}{T_1}[/tex]

[tex]p_2[/tex] = [tex]\frac{(204)(310)}{296}[/tex]

[tex]p_2[/tex] = [tex]\frac{63,240}{296}[/tex]

[tex]p_2[/tex] = 213.648 ≈ 213.65atm.

Therefore, the pressure inside the tank if left outside in the sun is 213.65atm.

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Every 557 years, the dwarf planet Eris revolves around the Sun. The average separation from the Sun is 67.7 a.u. (semimajor axis).

With an orbital period of 557 years, Eris is nearly at its closest point to the Sun, 96.6 AUs, as of 2011. Its perihelion occurred between 1698 and 1699, its aphelion occurred around 1977, and its perihelion will occur again between 2256 and 2258. At the aphelion position (approximately 152 million kilometers), the Sun-Earth distance is at its greatest, while at the perihelion position, it is at its shortest. The largest asteroid belt object between Mars and Jupiter is Ceres, the smallest of the five dwarf planets. However, Pluto is typically 39 AU, or 3.7 billion miles (5.9 billion kilometers), from the Sun. Pluto's closest approach to the Sun, or perihelion, occurred between 1979 and 1999.

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The radius in the circular path is 2m.

We are given that,

Acceleration = a = 32 m/s²

Speed = v = 4m/s

Thus , the radius of the circular path can be calculated by the formula,

a = v²/r

Where a is acceleration , v is speed and r is the radius of the circular path,

r = v²/a

r = (4m/s)²)/(32m/s²)

r = 2m

Hence the radius r of the circular path would be 2m.

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Observers need to look to the west to be able to see the highest constellation one month ago.

A constellation is a group of stars that appear connected to form a special configuration. In three-dimensional space, most of our stars have no relationship with each other but can appear as clusters on the night sky globe.

The constellation that was highest in the sky at midnight a month ago would be in the western sky at midnight, for its rise meant it had to rise earlier to get that far.

The Earth also orbits the Sun, causing different parts of the galaxy to appear at different points in Earth's orbit. This means that if you look at one group of stars one month, they will appear in a different place the next month.

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Upon calculation the molarity of H₂O₂ after four half lives if the initial concentration of H₂O₂ is 0.30M is found to be 0.01875 M

This question can be solved using the concept of first order reaction

Every reaction has its own tempo. A glass of milk will begin to get sour in approximately an hour if left on a sunny windowsill. But when potassium metal is added to water, it reacts quickly and strongly. Two factors affect how quickly a reaction occurs. The first is the rate constant (k), which varies depending on the kind of reaction and is temperature-dependent. The second factor is the reactant concentration. The sequence of the reactions determines how the concentration influences the rate.

For a first order reaction,

ln[tex](\frac{A}{A_{o} })[/tex]= Kt

here, A= initial concentration

[tex]A_{0}[/tex]= concentration at a time t

K= Rate constant

t= time

A= 0.30 M

ln[tex](\frac{A}{A_{0} })[/tex]= k× 4[tex]t_{1/2}[/tex]

ln([tex]\frac{0.30}{A_{o} }[/tex])= k×[tex]\frac{4 ln2}{k}[/tex]

[tex]\frac{0.30}{A_{0} }[/tex]= 2⁴

[tex]\frac{0.30}{16}= A_{0}[/tex]

[tex]A_{0}[/tex]= 0.01875M

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The amount of heat that the water absorbs in cooling system of the automobile is 4688320 Joules.

The water holding capacity of the cooling system of the automobile s 16L.

The density of water is 1000Kg/m³. The specific heat of water is 4.186  J/KgC°.

The temperature of the water rises to 87°C from 17°C.

Now, the amount of heat that the water absorbs is,

Q = mcT

Where,

Q is the heat absorbed,

m is the mass of the water,

c is the specific heat of water,

T is the change in temperature of water.

Putting values,

Q = 1000 x 16 x 4.186 x 70

Q = 4688320 Joules.

So, the amount of heat absorbed is 4688320 Joules.

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The moment about AB using the position vector AC is 55.9 i + 342.3 j + 0 k N.m and the position vector from A to C, calculate the moment about segment AB due to force F is -95.4 i + 191.07j + 0 k N.m.

Given that:

x₁ = 1.4m

y₁ = 1.7m

z₁ = 1.5m

Applied force at point C = F = | - 165 i  + 100 j + 140 k | N

The moment about AB using the position vector AC :

Using the equation: M(AB) = u(AB) . [ r(AC) X F ]        (equation 1)

We have:

OA = 0

OB = 1.4 i + 1.7 j

OC = 1.4 i + 1.7 j + 1.5 z

Now,

vector AB = vector OB - vector OA

vector AB = 1.4 i + 1.7 j

and, u(AB) = vector AB | vector AB     (equation 2)

= |vector AB| =

= AB  

= √ ( 1.4² + 1.7² )    (inserting this in equation 2)

= u(AB)  = (1.4 i + 1.7 j ) / √ ( 1.4² + 1.7² )

= u(AB) = 0.636 i + 0.772 j

distance r(AC) =  vector OC - Vector OA

= r(AC) = 1.4 i + 1.7 j + 1.5 z

Now, inserting values of u(AB), r(AB) and F in equation 1,

= M(AB) = 0.636 [1.7 X 140 - 1.5 X 100] + 0.772[1.4 X 140 + 165 X 1.5] + 0

= M(AB) = 0.636 (238 - 150) + 0.772(196 + 247.5) + 0

= M(AB) = 55.9 i + 342.3 j + 0 k N.m

Now,

r(BC) = vector OC - vector OB

r(BC) = (1.4 i + 1.7 j + 1.5 z) - (1.4 i + 1.7 j )

r(BC) = 1.5 z

Now, inserting values of u(AB), r(BC) and F in equation 1,

= M(AB) = 0.636 [0 X 140 - 1.5 X 100] + 0.772[ 0 X 140 + 165 X 1.5] + 0

= M(AB) = 0.636 (0- 150) + 0.772(0+ 247.5) + 0

= M(AB) = -95.4 i + 191.07j + 0 k N.m

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The complete question:

Calculating the moment about AB using the position vector AC

Using the position vector from A to C, calculate the moment about segment AB due to force F .

Express the individual components to three significant figures, if necessary, separated by commas.

The dimensions are: x₁ = 1.4m, y₁ = 1.7m, z₁ = 1.5m and the force applied at point C = [-165 i + 100 j + 140 k] N.

A uniform steel beam is suspended from one end on the construction  site of a new skyscraper. The beam's length is 0.99 m if its back-and-forth motion has a period of 2.00 s.

A simple pendulum is a beam suspended from one end. Simple pendulums are mechanical devices that move in a predictable pattern.

The formula for the time period of a simple pendulum whose length is 'l' is

T = 2[tex]\pi[/tex] [tex]\sqrt{\frac{l}{g} }[/tex]

Here, g is the acceleration due to gravity.

The time period of the beam is given as 2.00 s.

We can deduce from the preceding formula that

l = [tex]\frac{T^{2}g }{4\pi ^{2} }[/tex]

We have gravity acceleration, g = 9.8 m/[tex]s^{2}[/tex]

π = 3.14

and T = 2.00 s

So,

l= [tex]\frac{(2.00)(2.00)(9.8)}{4(3.14)(3.14)}[/tex]

or,

l = [tex]\frac{39.2}{39.4}[/tex]

or, l = 0.99 m.

As a result, the length of the beam is 0.99 m.

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Answer:

The answer is: It cannot be zero.

Explanation:

Displacement is the change in position of an object. Displacement can be 0 because the object just wouldn't move and its initial position and final position remain the same.

The vector size→a Along X -axis is 2 When Mets size along with j -axis is 0

So the vector → a will be → a = 2^Me+0^j.

vector size → b Along X -axis is 0

When t size along with j-axis is−2

When ts so the vector → b will be →b = 0^− 2 ^j.

A vector represents movement from one point to another. Vector quantities have both direction and magnitude. A scalar quantity has only one quantity. A vector can be represented by a line segment with an arrow think about the problem

The f-vector has the results of the other two vectors. According to the parallelogram law of vector addition.

Let f be the resultant force of d and e

that's why,

d+e=f

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The pressure inside the tank would be 213.65 atm.

According to  Gay-Lussac's law, for a particular gas, the pressure of the gas is directly proportional to the temperature at a constant volume.

p ∝ T: where p is the gas's pressure and T is the gas's Kelvin temperature.

Given that:

initial temperature: T₁ = 23° C =273 + 23 K = 296 K.

initial pressure: p₁ = 204 atm.

final temperature: T₂ = 37° = 273 + 37 K = 310 K.

final pressure: p₂ = ?

Now: according to Gay-Lussac's law:

p₂/T₂ = p₁/T₁

p₂ = p₁ (T₂/T₁)

= 204 ( 310/296) atm.

= 213.65 atm.

Hence, the pressure inside the tank would be 213.65 atm.

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The kinetic energy would increase by a factor of 25.

The kinetic energy of a moving body is a function of its mass and the velocity with which it is traveling. It can be expressed by the formula:

KE=1/2mu²

This suggests that the kinetic energy a body has varies directly with mass and with the square of the velocity. With this knowledge, we can easily figure out how it changes when the speed is altered by a certain factor. Assuming that the initial speed of a body of mass m was u, the initial kinetic energy of the body would be:

KE = 1/2mu²

Now that the speed is increased by a factor of of 5, the final speed y would be equal to 5 times the initial speed u, such that v=5u. The kinetic energy of the body would then be:

KE = 1/2m²

KE = 1/2m(5u)

KE = 1/2m(252)

Pulling out 25 and replacing the expression for the initial kinetic energy:

KE = 25.1/2mu²

KE = 25KE

So, on increasing the velocity by a factor of 5, the kinetic energy would increase by a factor of 25.

Kinetic energy is the energy possessed by an object caused by the force of motion. The term kinetic comes from the Greek, 'kinetikos', which means to move. Therefore, an object moving at a certain speed must have kinetic energy, while an object that is not moving does not have kinetic energy.

Kinetic energy is also called motion energy, where the movement of an object can produce other energy. For example, motion energy can be turned into electrical energy, eventually that electrical energy can be utilized by humans.

Kinetic energy is divided into two types which are classified based on the movement of an object, namely:

This type of translation is kinetic energy produced by objects moving in a straight line with the same direction and speed. For example, a car driving on a highway and a bullet moving in a straight line.

This is a condition when an object rotates. When rotating, the amount of energy in it can change. For example, the rotation of the earth around the sun, a spinning top that rotates on its axis, and a Ferris wheel.

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A amount of water corresponding to the submerged lead's own volume is displaced by it, and A volume of water equal to the weight of the floating lead is displaced by the floating lead.

A measured amount of rigidity, a fundamental characteristic of all matter, is known as mass in physics. The resistance an unit of matter gives to one change in its pace or location as a result of the applying of a force is what it is in essence.

(a) A body's mass is how much matter is there inside of it. Kg is really the SI mass measurement unit. (kg). (b) The force that pulls a body toward the center of the earth is the load of that body.

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Answer:

It slows down.

Explanation:

When light travels from one medium to another, its speed changes according to the properties of the two media. In the case of light traveling from air to water, the speed of light will decrease. This is because water is denser than air, so the light waves encounter more resistance as they pass through the water. This causes the light to slow down and its path to bend, a phenomenon known as refraction.

Answer: It slows down.

Explanation:

they are said to be “denser” than air. what happens is that light slows down when it passes from the less dense air into the denser glass of water. this slowing down the ray of light also causes the ray of light to change directions. it is the change in the speed of the light that causes refraction.

The index of refraction of water (1.33) is greater than that of air (1.00).

With that said the index of refraction is related to the velocity of light by:

[tex]n=\frac{c}{v}[/tex]

where n is the index of refraction, c is the speed of light in a vacuum and v is the velocity of light in the medium.

As c is constant we can see that the speed of light in a medium is inversely proportional to the index of refraction

[tex]n = \frac{1}{v} \\[/tex]

therefore the medium with the lower index of refraction will have the greatest velocity of light (Air).

A bird of 2Kg mass was flying at 4m/s towards a car and the car of mass 12000 Kg was going with 30m/s towards the bird, then the velocity of center of mass is 11250.35m/s

Given the mass of bird(m1) = 2kg

Mass of car (m2) = 12000kg

velocity of bird (v1) = 4m/s

velocity of car (v2) = 30m/s

Velocity of center of mass (V) = m1v1 + m2v2 / m1+m2

V = 2x4 + 12000x30 / 2+30 = 11250.35m/s

Hence the velocity of center of mass is 11250.35m/s

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The pooled estimated value of p is 0.435

Given values

n1 = 100

n2 = 100

x1 = 42  and  x2 = 45

H0: p1 = p2  

Calculation:

p1 = [tex]\frac{x_1}{n_1}[/tex]

=> 42/100

=>0.42

so p1=0.42

p2= [tex]\frac{x_2}{n_2}[/tex]

=> 45/100

=>0.45

so shown that p1 ≠ p2 so the claim that p1 = p2 is false and proved above using two tail test.

p = [tex]\frac{x_1+x_2}{n_1+n_2}[/tex]

=>(42+45)/(100+100)

=>87/200

=>0.435

so p = 0.435

The pooled estimate p. is 0.435

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Complete question :

Assume that you plan to use a significance level of α = 0.05 to test the claim that wheather p1 = p2. Use the sample sizes mentioned  below  and numbers of successes to find the pooled estimate p. Round your answer to appropriate decimal.

Given values:

n1 = 100, n2 = 100 ,x1 = 42 ,x2 = 45

Joe throws his ball vertically upward with an initial speed twice as high as the Bill. The maximum height of Joe's ball is 4 times of the maximum height of Bill's ball.

The equation of motion for the upward vertical motion is:

v² = u² - 2.gh

Where

v = final velocity

u = initial velocity

h = height

g = acceleration due to gravity

At the maximum height, the final speed is zero, hence:

0 = u² - 2.gh

u² = 2.gh

Therefore, the maximum height is directly proportional to the square of initial speed.

In the problem, u_joe =  2 x u_bill

Hence,

(u_joe)² : (u_bill)² = h_joe : h_bill

(2xu_bill)² : (u_bill)² = h_joe : h_bill

h_joe : h_bill = 4 : 1

Thus, the maximum height of Joe's ball is 4 times of the maximum height of Bill's ball.

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The number of collisions is 26. An elastic collision is one in which the system does not experience a net loss of kinetic energy as a result of the collision.

Two objects collide in an elastic collision when no kinetic energy is wasted. The kinetic energy and momentum of the objects are conserved when they bounce back from one another. We are dealing with an elastic collision because inelastic collisions are thought to happen when the two items stay together after the collision.

Initial energy equals E o

=2MeV=2×10 6 \s eV

After the initial collision, E 1 = 2 E o

​After a second collision, E 2 equals 2 E 1.

​​ \s = \s2 \s2

E \so \s​

When there is a third collision, E 3 equals 2 E 2.

​​ \s = \s2 \s3

E \so \s​

And so

Following n collisions, E n = 2 n

E \so \s​

final energy = 0.04 eV

Consequently, E n = 0.04

⟹ \s2 \sn

2×10 \s6

​ \s =0.04

⟹2 \sn \s = \s0.04 \s2×10 \s6

​ \s =5×10 \s7

n=log 2 (510 7 )=log 10 2 log 10 (510 7 )

​⟹n= \s0.301 \s7+0.699

​⟹n=26

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Answer:

0.59 seconds

Explanation:

To find the time it takes for a tennis ball to reach the ground and bounce back to a height of 7 meters, we need to use the formula for the time it takes an object to fall to the ground.

The formula for the time it takes an object to fall to the ground is given by:

t = sqrt(2 * d / g)

where t is the time it takes the object to fall, d is the distance the object falls, and g is the acceleration due to gravity.

In this case, we are given that the height from which the tennis ball is dropped is 3 meters, the height to which the ball bounces is 7 meters, and the acceleration due to gravity is 9.8 m/s^2. We can use these values to solve for the time it takes for the ball to reach the ground and bounce back to a height of 7 meters.

First, we need to calculate the distance the ball falls. The distance the ball falls is equal to the difference between the height from which the ball is dropped and the height to which the ball bounces:

d = H1 - H2

d = 3 - 7

d = -4

Next, we can use the formula for the time it takes an object to fall to the ground to solve for the time it takes for the ball to reach the ground and bounce back to a height of 7 meters:

t = sqrt(2 * d / g)

t = sqrt(2 * -4 / 9.8)

t = 0.59 seconds

Therefore, it takes 0.59 seconds for the tennis ball to reach the ground and bounce back to a height of 7 meters.