i NED HELP i’m so confused

Answer:

Explanation:

height of the building h = 15 m

initial vertical velocity u = 0

v² = u² + 2 g h

u = 0 , final velocity after falling height h

h = 15

v² = 2 x 9.8 x 15

v = 17.14 m /s

. Time of fall be t

h = 1/2 g t²

15 = 1/2 x 9.8 x t²

t = 1.749 s

This time will be required for truck to come under the building .

speed = distance / time

distance = speed x time

= 22 x 1.749

38.5 m

Truck should be at a distance of 38.5 m . when the stuntman starts falling .

Part A: The time required to hit the truck by a stuntman is 1.749 s.

Part B: The distance between the building and truck is 38.47 m.

Given that the height h of the building is 15 m. The constant speed s of driving the truck is 22 m/s.

Part A

The final velocity can be calculated by the formula given below.

[tex]v^2 = u^2 + 2gh[/tex]

Where v is the final velocity, u is the initial velocity, g is the gravitational acceleration and h is the height of the building.

The initial velocity u will be zero and g = 9.8 m/s2.

Substituting the values,

[tex]v^2 = 0 + 2\times 9.8\times 15[/tex]

[tex]v^2 = 294[/tex]

[tex]v = 17.14 \;\rm m/s[/tex]

The time to hit the truck can be calculated as given below.

[tex]h = ut + \dfrac {1}{2}gt^2[/tex]

[tex]15 = 0 + \dfrac {1}{2}\times 9.8 \times t^2[/tex]

[tex]t^2 = 3.06[/tex]

[tex]t = 1.749 \;\rm s[/tex]

Hence we can conclude that the time required to hit the truck by stuntman is 1.749 s.

Part B

The distance between the building and truck is calculated as given below.

[tex]d = s \times t[/tex]

[tex]d = 22 \times 1.749[/tex]

[tex]d =38.47\;\rm m[/tex]

Hence the distance between the building and truck is 38.47 m.

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Answer:

0.9 Amps

Explanation:

Ohm's law: Voltage = Current x Resistance

Rearrange equation:

Current =Voltage/Resistance

Voltage=6v

In a series circuit the total resistance is the sum of all the resistors so the total resistance = 0.1+0.15+0.2+0.25+6=6.7 Ohms

6/6.7 = 0.9 (1dp) Amps

Because it is a series circuit, the current is the same throughout the entire circuit, all the resistors have a current of 0.9 Amps.

Hope this helped!

Complete Question

What mass of aluminum has a total nuclear charge of 2.9 C?

Aluminum has atomic number 13. Suppose the aluminum is all of the isotope with 14 neutrons.

Answer:

The  mass is   [tex]T_m  = 6.252 *10^{-5}\  g[/tex]

Explanation:

From the question we are told that

   The  total nuclear charge is  [tex]q =  2.9 \  C[/tex]

   The  atomic number is  [tex]u  =  13[/tex]

    The number of neutron is  [tex]k  =  14[/tex]

Generally the number of positive charge is mathematically represented as

      [tex]N  = \frac{q}{p}[/tex]

here p is the charge on a single proton with value  [tex]p =  1.60*10^{-19} \  C[/tex]

So      

     [tex]N = \frac{2.9}{1.60*10^{-19}}[/tex]

=>    [tex]N = 1.813*10^{19} \ protons[/tex]

Now since 1 atom contains 13 proton

The  number of atoms present is

        [tex]a =  \frac{1.813*10^{19}}{13}[/tex]

       [tex]a =  1.395 *10^{18} \  atoms[/tex]

Then the number of moles present is mathematically represented as

      [tex]n = \frac{a}{N_k}[/tex]

Where  N_k is the Boltzmann constant with value  

       [tex]N_k  =  6.023*10^{23}[/tex]

So

       [tex]n  =  \frac{1.395 *10^{18}}{ 6.023*10^{23}}[/tex]

        [tex]n = 2.315 *10^{-6}\  moles[/tex]

Generally one mole of aluminum is equal to 27 g

So

 The total  mass of aluminum  is

          [tex]T_m  = n *  27[/tex]

=>        [tex]T_m  = 2.315 *10^{-6}  *  27[/tex]

=>        [tex]T_m  = 6.252 *10^{-5}\  g[/tex]

Answer:

Option B

200 cm

Explanation:

From statistical evidence, the average height of an adult is about 200cm. This is like 2m or 6.56 feet.

Despite the fact that there are some exceptions; with some adults reaching heights of about seven feet, and some dwarfs who stand only about 1 m tall,  most adults only grow to about 200cm in height before they start shrinking due to old age.

Answer:

Fe = 9 x 10⁻⁹ N

Fg = 3.97 x 10⁻⁴⁶ N

Fe = 2.26 x 10³⁷ Fg

Explanation:

First we find electric force by Coulomb's Law as follows:

Fe = kq₁q₂/r²

where,

Fe = electric force = ?

k = Coulomb's Constant = 9 x 10⁹ N.m²/C²

q₁ = q₂ = charges on electron and proton = 1.6 x 10⁻¹⁹ C

r = distance between electron and proton = 1.6 x 10⁻¹⁰ m

Therefore,

Fe = (9 x 10⁹ N.m²/C²)(1.6 x 10⁻¹⁹ C)(1.6 x 10⁻¹⁹ C)/(1.6 x 10⁻¹⁰ m)²

Fe = 9 x 10⁻⁹ N

Now we find gravitational force by Newton's Law of Gravitation as follows:

Fg = Gm₁m₂/r²

where,

Fg = gravitational force = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

m₁ = mass of electron = 9.11 x 10⁻³¹ kg

m₂ = mass of proton = 1.673 x 10⁻²⁷ kg

r = distance between electron and proton = 1.6 x 10⁻¹⁰ m

Therefore,

Fg = (6.67 x 10⁻¹¹ N.m²/kg²)(9.11 x 10⁻³¹ kg)(1.673 x 10⁻²⁷ kg)/(1.6 x 10⁻¹⁰ m)²

Fg = 3.97 x 10⁻⁴⁶ N

Dividing both forces:

Fe/Fg = (9 x 10⁻⁹ N)/(3.97 x 10⁻⁴⁶ N)

Fe = 2.26 x 10³⁷ Fg

The electric force is 2.3 × 10^39 times greater than the gravitational force.

The gravitational force between the proton and the electron is obtained from;

Fg = Gmemp/r^2

Where;

me = mass of the electron

mp = mass of the proton

r = distance of separation

Fg = 6.67 × 10^−11  × 9.11 × 10^−31 × 1.673 × 10^−27/(1.6 × 10^−10)^2

Fg = 3.94 × 10^−48 N

For the electric force;

Fe= K e^2/r^2

K = electric constant

e = magnitude of charge on electron and proton

r = distance of separation

Hence;

Fe = 8.988 × 10^9 × (1.602×10^−19)^2/(1.6×10^−10)^2 =

Fe = 9 × 10^−9 N

The number of time the electric force is stronger than the gravitational force = 9 × 10^−9 N/3.94 × 10^−48 N = 2.3 × 10^39 times

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Answer:

A. Using

Pgauge= Pmanometer

And we know that

Pgauge= deta(hpg)

So deta h = Pgauge/density x g

So

= 7.5(6894.76/1psig)/ 13.6*10^3*9.8m/s²)

= 387.9mm

So to find height of pipe connected to the pipe we say

= h -deta h

= 900-387.97mm

=512.02mm

B. We use manometry principle

Pgas+density xg(25*10^3)-PX density{h-(H-0.25)=0

So

Finally Pgas= 6.54psig

3.56 displacement ( m )

Answer:

t the apparent weight of the body decreases when it is submerged in water,

 F'_{e} = mg - ρ_liquid g V

Explanation:

When a container is placed on a scale it falls due to the weight of the body and the needle attached to the spring shows the value of the weight that is proportional to the displacement of the spring.

When the body is immersed in a container with water, it exerts a push on the body, so its apparent weight decreases and the compression of the scale is less, therefore it indicates a smaller weight of the body.

Let's write the equilibrium equation for the body is placed on the scale without water

               [tex]F_{e}[/tex] - W = 0

               F_{e} = W

Let us propose the equilibrium equation for this case

            F'_{e} + B - W = 0

where F'_{e} is the elastic force, B the push of the liquid and W the weight of the body

            F'_{e} = W -B

The thrust of the liquid is given by the Archimedean principle which says that it is equal to the weight of the dislodged liquid

            B = ρ g V

             F'_{e} = mg - ρ_liquid g V      (1)

we use the density concept

            ρ_body = m / V

we substitute

             F'_{e}= g V (ρ_body - ρ_agua)          (2)

             F'_{e} < F_{e}

We see  from expression is 1 and 2 that the apparent weight of the body decreases when it is submerged in water,

To know the specific value of the decrease, the weight of the body in the air or its density and volume must be known

Answer:

732492 g

Explanation:

Given that

Room Temperature = 300 K

Cold T = 0°C = 0 + 273 =273 K

Work done = 0.375 hp

ΔH of fusion of water is 6008 J per mol

The first thing we do is to Convert the power into J/s

Given that 1 hp = 746 W (J/s), then

0.375 hp = 0.375 * 746 W/hp

0.375 = 280 J/s

Then we find the heat per unit time

Q = (cold T / hot T - cold T ) x power

Q = [273 / (300 - 273)] * 280

Q =273/27 * 280

Q = 10.1

Q = 2831 J/s

Moles of ice per second = Q/ ΔH fusion

Moles of ice per second = 2831/6008 = Moles of ice per second = 0.471 mol /s

If we convert 1 day into second, we have

1 day = 1 day * ( 24 hours/day) * ( 60 minutes/hour) * (60 seconds/minutes)

1 * 24 * 3600 = 86400 second

moles of ice /day

0.471 mol / s ) x 86400 s / day =

40694 mols of ice

Molar mass is 18 g/mol

Mass of ice

40694 * 18 = 732492 g

Mass of ice produced per day is 732492 g

Answer:

The  value is  [tex]u_1 =  236 \ m/s[/tex]

Explanation:

From the question we are told that

   The  mass of bullet  is  [tex]m_b  =  0.0125 \  kg[/tex]

   The  mass of the block is  [tex]M_B  =  0.240 \  kg[/tex]

    The  spring constant is  [tex]k  =  2.25*10^{3} \  N/m[/tex]

   The  amplitude is  [tex]A= 12.4 \ cm  =  0.124 \ m[/tex]

Generally according to the conservation of momentum is  

     [tex]m_b u_1 + M_B  u_2 =  (m_b + M_B) v[/tex]

given that the block was at rest we have that

        [tex]m_b u_1  =  (m_b + M_B) v[/tex]

Now the angular velocity of the both bodies is mathematically represented as

     [tex]w =  \sqrt{\frac{k}{M_B  + m_b} }[/tex]

          [tex]w = \sqrt{\frac{ 2.25*10^{3}}{ 0.0125 + 0.240 } }[/tex]

         [tex]w =  94.4 \  rad/s[/tex]

Given that the system after collision set into oscillation

The maximum  linear velocity of the system after impact  is mathematically represented as

       [tex]v  = A * w[/tex]

      [tex]v  =  94.4 *0.124[/tex]

      [tex]v  =  11.7 \  m/s[/tex]

From above equation

    [tex]u_1  =  \frac{(m_b +  M_B ) * v}{m_b}[/tex]

=>    [tex]u_1 =  \frac{(0.240 + 0.0125) *  11.7}{ 0.0125}[/tex]

=>   [tex]u_1 =  236 \ m/s[/tex]

Answer:

Special relativity.

Explanation:

Einstein's general theory of special relativity describes the relationship

between energy and matter, and is major event in the history

of science.

In 1905, Albert Einstein a noble physicist developed a theory that forms part of the basis of modern physics and one of the major event in the history of science, this theory was known as the theory of special relativity.

The theory of special relativity gives the relationship between space and time for any object that is moving at a uniform speed in a straight line, typically at the speed of light.

Simply stated, the theory of special relativity describes how a change in the speed of an object affect or relate with the measurement of space, time and mass. This ultimately implies that, as an object approach the value of light speed, it gains an infinite amount of mass and as such it is unable to travel faster than light.

The theory of special relativity by Albert Einstein gave birth to one of the most famous equation in science;

[tex]E = mc^2[/tex]

The equation illustrates, Energy equals mass multiplied by the square of the speed of light.

Where; E = Energy.

M = Mass.

C = Speed of light.

From the above equation, we can deduce that the mass of an object increases with speed and that mass is equivalent to energy, thus matter (mass) can be interchanged with energy.

Answer:

Explanation:

In this problem, we are required to solve for the total distance that the car travelled. and the displacement

A) the distance travelled by car

this can be gotten by summing all the distances the car has travelled.

i,e total distance= 60 miles+120 miles

total distance= 180 miles

B) the displacement of the car

the displacement can be gotten by  subtracting the final distance from the initial distance

final distance = 120 miles

initial distance= 60 miles

displacement= 120-60= 60 miles

Answer:

There are eight planets in our Solar System.

Explanation:

Answer:

8

Explanation:

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune

Answer:

An virus

Explanation:

An computer virus can come from websites that try to steal your Information or apps that's not necessarily scanned and protected so that yor computer can be safe from viruses.

A computer may encounter problems or get "ill" for a variety of reasons. The system can become infected with malware and viruses, which can cause performance issues and data loss.

A failing hard drive or defective RAM are examples of hardware issues that can lead to instability and crashes. Overheating can lead to hardware damage or performance deterioration and is frequently brought on by insufficient cooling or clogged air vents.

Systems may become unstable as a result of software conflicts between out-of-date or incompatible programmes.

Electrical problems or power surges can harm components and interfere with proper operation. Computer issues can also be caused by human error, such as inadvertent file deletion or poor configuration.

Thus, a computer can be kept in good condition with routine maintenance, security precautions, and appropriate usage.

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Explanation:

The expression is :

[tex]A=B^nC^m[/tex]

A =[LT], B=[L²T⁻¹], C=[LT²]

Using dimensional of A, B and C in above formula. So,

[tex]A=B^nC^m\\\\\ [LT]=[L^2T^{-1}]^n[LT^2}]^m\\\\\ [LT]=L^{2n}T^{-n}L^mT^{2m}\\\\\ [LT]=L^{2n+m}T^{2m-n}[/tex]

Comparing the powers both sides,

2n+m=1 ...(1)

2m-n=1 ...(2)

Now, solving equation (1) and (2) we get :

[tex]n=\dfrac{1}{5}\\\\m=\dfrac{3}{5}[/tex]

Hence, the correct option is (E).

The values of the exponents n and m are [tex]\frac{1}{5}[/tex] and [tex]\frac{3}{5}[/tex] respectively.

The given parameters;

[tex]A = B^nC^m[/tex]

[tex]A = LT\\\\B = L^2T^{-1}\\\\C = LT^2[/tex]

The values of the given exponents "n" and "m" are calculated as follows;

[tex]LT = [L^2T^{-1}]^n[LT^2]^m\\\\LT= [L^{2n}T^{-n}][L^mT^{2m}]\\\\LT = [L^{2n + m} \ T^{2m-n}]\\\\L^1 = L^{2n + m} \\\\T^1 = T^{2m-n}\\\\1 = 2n \ + m \ ---(1)\\\\1 = 2m - n \ ---(2)[/tex]

from equation(2);

[tex]n = 2m - 1[/tex]

substitute the value of n into equation (1);

[tex]1 = 2(2m-1) + m\\\\1 = 4m - 2 + m\\\\1 = 5m - 2\\\\3 = 5m\\\\m = \frac{3}{5} \\\\n = 2m - 1\\\\n = 2(\frac{3}{5} ) - 1\\\\n = \frac{6}{5} - 1 \\\\n = \frac{1}{5}[/tex]

Thus, the values of the exponents n and m are [tex]\frac{1}{5}[/tex] and [tex]\frac{3}{5}[/tex] respectively.

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Answer:

With this analysis the correct answer is

Metal bar. The answer is uniform charge  distribute

Non-metallic bar. As we see the charge of the ball, at the ends closest to the ball a charge of the same sign as the ball and at the far end the charge of equal magnitude and opposite sign

Explanation:

When the ball touches the bar, a charge transfer process occurs, leaving half in the bar and the other half in the ball, when the ball bounces and clears it, two dependent processes can occur, the bar is metallic or non-metallic , let's analyze the two cases

* metal bar, the load that is on the bar is distributed evenly throughout the bar, with each bounce of the ball the load on the bar increases and decreases in the balls until the two loads are equal and appear from this rebound no there is more load transfer

* Non-conductive insulating bar, when the ball touches the bar for the first time, it creates a load equal to q / 2, when the ball moves away from the bar, for this non-conductive, the transferred load remains in the same place. Therefore this load induces a load of equal magnitude, but opposite sign at the other end of the bar.

When the ball approaches for the second time, the opening already has a load, therefore the amount of load deposited is less, with between processes in each bounce the bar of the bar sounds, the process continues until the load of the ball and the bar have been equal.

With this analysis the correct answer is

Metal bar. The answer is uniform charge  distribute

Non-metallic bar. As we see the charge of the ball, at the ends closest to the ball a charge of the same sign as the ball and at the far end the charge of equal magnitude and opposite sign

Answer:

e) electrons are transferred from the rod to the silk.

Explanation:

An initially neutral glass rod contains equal number of electron and proton.

If the rod becomes positively charged  after being rubbed with silk, then the rod must have lost some its electron to the silk since electrons are more mobile than protons, leaving the rod with excess positive charge (protons), and the silk will be negatively charged (excess electron).

Thus, the rod becomes positively charged by transfer of electrons from rod to the silk.

e) electrons are transferred from the rod to the silk.

Answer:

50km/h

Explanation:

Average velocity = change in distance (or distance travelled) divided by/ the change in time (or time taken.)

The change in distance has been given as 100km.

The change in time is 3pm-1pm = 2 hours.

Therefore the average velocity was 100/2 = 50km/h (to the east).

Hope this helped!

The given expression 3 + 2 ∙ 4 = 3 + (2 ∙ 4) is absoulutely correct so it is True.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

3 + 2 ∙ 4 = 3 + (2 ∙ 4)

We know that in every calculation we cannot separate multiplication and need to solve them first

So,

3 + 8 = 3 + 8

11 = 11

Hence, 3 + 2 ∙ 4 = 3 + (2 ∙ 4)  is absoulutely correct.

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Answer:

The task of philosophy, for Plato, is to discover through reason (“dialectic”) the nature of the Forms, the only true reality, and their interrelations, culminating in an understanding of the most fundamental Form, the Good or the One. Aristotle rejected Plato’s theory of Forms but not the notion of form itself. For Aristotle, forms do not exist independently of things—every form is the form of some thing. A …

Explanation:

Answer:

Beat frequency together = 2.95 Hz (Approx)

Explanation:

Given:

Frequency (F) = 294 H

Decrease in tension = 2%

Find:

Beat frequency together

Computation:

Tension = (100 - 2) / 100

Tension (T) = 0.98

Beat frequency together = Frequency (F) - (√T × F)

Beat frequency together = 294 - (√0.98 × 294)

Beat frequency together = 2.95 Hz (Approx)

The beat frequency heard when the two strings are played together is 2.95 Hz.

Given data:

The tuning frequency of the violin is, f = 294 Hz.

Decrement in the tension is, 2 %.

Since, tension is reduced at the rate of 2%. Then the new magnitude of tension on the string is,

T = (100 - 2 )/100

T = 0.98

Then the expression for the beat frequency heard when the two strings are played together is given as,

[tex]f_{b}=f -(\sqrt{T \times f})[/tex]

Solving as,

[tex]f_{b}=294-(\sqrt{0.98 \times 294})\\\\f_{b}=2.95\;\rm Hz[/tex]

Thus, we can conclude that the beat frequency heard when the two strings are played together is 2.95 Hz.

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Answer:

Given initial height h¹= 1.44

Final height h²=1.68

So factor increase is 1.68/1.44²= 1.17

Percentage increase will be

1.68-1.44/1.44*100%=16.7%

Answer:

C. Diffraction

Explanation:

Diffraction is the bending of waves as they pass by a barrier or through an opening. One of the condition for diffraction is that the size of the aperture or obstacle is comparable to the wavelength of light. Fresnel diffraction and Fraunhofer diffraction are two types of diffraction.

Hence, the correct option is (c) "Diffraction".

Answer:

a

[tex]N  =  2.094*10^{10} \  electrons[/tex]

b

[tex]O  =  9.33*10^{-13} \  electrons[/tex]

Explanation:

From the question we are told  that

   The  mass of the lead sphere is  [tex]m  =  7.70g =  0.0077 \  kg[/tex]

   The net charge is [tex]Q_{net} =  -3.35*10^{-9} \ C[/tex]

   The  atomic number is  [tex]u  =  82[/tex]

     The  molar mass is  [tex]M  =  207 \  g/mol[/tex]

Generally the excess number of  electron on the sphere is mathematically represented as

     [tex]N  =  \frac{Q_{net}}{ e }[/tex]

Here e is the charge on the electron is [tex]e  =  -1.60 *10^{-19} \  C[/tex]  

     So

    [tex]N  =  \frac{-3.35 *10^{-19}}{ -1.60*10^{-19}}[/tex]

     [tex]N  =  2.094*10^{10} \  electrons[/tex]

Generally the number of atom present is mathematically represented as  

     [tex]n  =  N_a  *  \frac{m}{ M}[/tex]

Here [tex]N_a[/tex] is the Avogadro's number with value  [tex]N_a  =  6.0*10^{23} \  atoms[/tex]

       [tex]n  =  6.03 *10^{23} *  \frac{7.70}{ 207}[/tex]

      [tex]n  =  2.24 *10^{22} \  atoms [/tex]

Generally the electrons are there per lead atom is mathematically represented as

       [tex]O =  \frac{N}{n}[/tex]

=>   [tex]O =  \frac{2.24*10^{22}}{2.094*10^{10}}[/tex]

=>    [tex]O  =  9.33*10^{-13} \  electrons[/tex]

Answer:

3.15 N towards the positive x-axis

Explanation:

first charge has charge q1 = 10 μC = 10 x 10^-6 C

second charge has charge q2 = 20 μC = 20 x 10^-6 C

third charge has charge q3 = -30 μC = -30 x 20^-6 C

According to coulomb's law, force between two charged particle is given as

F = [tex]\frac{-kQq}{r^2}[/tex]

Where

F is the force between the charges

k is Coulomb's constant = 9 x 10^9 kg⋅m^3⋅s^−2⋅C^−2.

Q is the magnitude of one charge

q is the magnitude of the other charge

is the distance between these two charges

For the force on q2 due to q1,

distance r between them = 0 - (-1.0) = 1 m

F = [tex]\frac{-9*10^{9}*10*10^{-6}*20*10^{-6}}{1^2}[/tex] = -1.8 N (the negative sign indicates a repulsion on q2 towards the positive  x-axis)

For the force on q2 due to q3,

distance between them = 2.0 - 0 = 2 m

F = [tex]\frac{-9*10^{9}*20*10^{-6}*(-30*10^{-6})}{2^2}[/tex] = 1.35 N (the positive sign indicates an attraction on q2 towards the positive x-axis)

Resultant force on q2 = 1.8 N + 1.35 N = 3.15 N towards the positive x-axis

Answer:

A. The wires exert equal magnitude attractive forces on each other.

Explanation:

Magnetic field due to current i on current 2i

B₁ = 10⁻⁷ x 2 i / r where r is distance between the two wires

Force on wire II due to wire I per unit length

= magnetic field x current in wire II

= B₁ x 2 i

= [ 10⁻⁷ x 2 i / r ]  x 2i

= 4  x 10⁻⁷ i² / r

Magnetic field due to current 2i on current i

B₂ = 10⁻⁷ x 4 i / r where r is distance between the two wires

Force on wire I due to wire II per unit length

= magnetic field x current in wire I

= B₂ x  i

= [ 10⁻⁷ x 4 i / r ]  x i

= 4  x 10⁻⁷ i² / r

So final forces on each wire are same .

This force will be attractive in nature . The direction of force can be known from fleming's right  hand rule .

Answer:

(A) The maximum height of the ball is 40.57 m

(B) Time spent by the ball on air is 5.76 s

(C) at 33.23 m the speed will be 12 m/s

Explanation:

Given;

initial velocity of the ball, u = 28.2 m/s

(A) The maximum height

At maximum height, the final velocity, v = 0

v² = u² -2gh

u² = 2gh

[tex]h = \frac{u^2}{2g}\\\\h = \frac{(28.2)^2}{2*9.8}\\\\h = 40.57 \ m[/tex]

(B) Time spent by the ball on air

Time of flight = Time to reach maximum height + time to hit ground.

Time to reach maximum height = time to hit ground.

Time to reach maximum height  is given by;

v = u - gt

u = gt

[tex]t = \frac{u}{g}[/tex]

Time of flight, T = 2t

[tex]T = \frac{2u}{g}\\\\ T = \frac{2*28.2}{9.8}\\\\ T = 5.76 \ s[/tex]

(C) the position of the ball at 12 m/s

As the ball moves upwards, the speed drops, then the height of the ball when the speed drops to 12m/s will be calculated by applying the equation below.

v² = u² - 2gh

12² = 28.2² - 2(9.8)h

12² - 28.2² = - 2(9.8)h

-651.24 = -19.6h

h = 651.24 / 19.6

h = 33.23 m

Thus, at 33.23 m the speed will be 12 m/s