A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline.Masses are stacked on top of the block until the top of the block is level with the waterline. This requires 20 g of mass. What is the mass of the wooden block?A.) 40 gB.) 20 gC.) 10 g

Answer:

increase

Explanation:

think of climbing a mountain. the higher you go the harder it is to breathe. its because air pressure is increasing

Answer:

decrease.

Explanation:

The air pressure is given by

P = h x d x g

where, h is the height of air column above the surface and g be the acceleration due to gravity and d be the density of air.

As we go up, the height of air column decreases, density of air decreases and acceleration due to gravity also decreases, so the value of pressure decreases at altitudes.

Answer:

initial and final temperatures of both the water and metal, mass of the metal, and mass of the water

Explanation:

Heat lost by the metal, [tex]Q = mc(t_{2} - t_{1})[/tex]

Heat gained by the water in the calorimeter, [tex]Q_{w} = m_{w}c_{w}(t_{2w} - t_{1w})[/tex]

For energy to be conserved in the system, the heat lost by the metal will equal the heat gain by the water in the calorimeter.

        [tex]mc(t_{2} - t_{1}) = m_{w}c_{w}(t_{2w} - t_{1w})[/tex]

Where,

m is the mass of the metal

c is specific heat capacity of the metal

t₂ is the final temperature of the metal

t₁ is the initial temperature of the metal

[tex]m_{w} [/tex] is the mass of the water

[tex]c_{w} [/tex] is specific heat capacity of water

[tex]t_{2w} [/tex] is the final temperature of water

[tex]t_{1w} [/tex] is the initial temperature of water

From the question given, specific heat capacity of the water is known, the quantities to be measured are;

Initial and final temperatures of both the water and metal,

Mass of the metal, and mass of the water

Answer:

Length of the stake will be 0.3623 m

Explanation:

We have given energy required to fully drive a stake into ground = 0.30 KJ = 300 J

Average resistive force acting on the floor is equal to F = 828 N

We have to find the length of the stake

We know that work done is given by

W = Fd, here W is work done , F is average force and d is the length of the stake

So 300 = 828×d

d = 0.3623 m

So length of the stake will be 0.3623 m

The length of the stake is approximately 0.362 meters.

To solve this problem, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done to drive the stake into the ground is equal to the potential energy gained by the stake when it is fully driven into the ground.

The work done (W) is given as 0.30 kJ, which is equal to 0.30 * 10^3 J.

The resistive force (F) is given as 828 N.

The distance (d) over which the work is done is the length of the stake.

We can use the formula for work:

[tex]\[W = F \cdot d\][/tex]

Rearranging the formula to solve for \(d\):

[tex]\[d = \frac{W}{F}\][/tex]

Substituting the given values:

[tex]\[d = \frac{0.30 \times 10^3 \, J}{828 \, N}\][/tex]

[tex]\[d = 0.362 \, m\][/tex]

The question requires arranging substances by density, a fundamental physics concept, calculated as mass divided by volume. Understanding densities, from light gases to dense neutron stars, is essential in both everyday applications and advanced scientific fields.

The question involves arranging substances in order of increasing density based on given masses and volumes. Density is the measure of how much mass is contained in a given volume, and this concept is fundamental in physics. By calculating the density of each substance using the formula density = mass/volume (expressed in g/cm³ for solids and liquids or g/L for gases), we can compare the densities of the substances and arrange them accordingly. It is crucial to recognize that the density of a material is a characteristic property that can help in identifying the material and understanding its behavior in different environments.

Density plays a significant role in various applications, such as determining whether an object will float or sink in a fluid, in material selection for construction, and in understanding the structure of the universe, from the density of air we breathe (1.2 g/L) to the dense core of neutron stars reaching up to 10¹⁵ g/cm³.

To arrange the substances in order of increasing density, we need to calculate the density of each substance using the formula [tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]

Then, we compare the calculated densities to determine their relative order.

Here's how the substances could be ranked:

1. Helium gas: Since helium gas is the least dense substance, it will have the lowest density.

2. Cork: Cork typically has a low density compared to other materials.

3. Water: Water has a moderate density, higher than helium gas and cork.

4. Aluminum: Aluminum generally has a higher density than water.

5. Iron: Iron is denser than aluminum, making it the densest substance among the listed ones.

By comparing the calculated densities, we can arrange the substances in increasing order of density from lowest to highest: helium gas, cork, water, aluminum, and iron.

Answer:

[tex]\overrightarrow{F} = -\left ( 15x^{4}y-3 \right )\widehat{i}-3x^{5}\widehat{j}[/tex]

Explanation:

[tex]U = 3x^{5}y-3x[/tex]

Force is defined as the

[tex]\overrightarrow{F} = -\frac{dU}{dx}\widehat{i}-\frac{dU}{dy}\widehat{j}[/tex]

[tex]\frac{dU}{dx}=15x^{4}y-3[/tex]

[tex]\frac{dU}{dy}=3x^{5}[/tex]

So, force is given by

[tex]\overrightarrow{F} = -\left ( 15x^{4}y-3 \right )\widehat{i}-3x^{5}\widehat{j}[/tex]

Answer:

The new electric field strength of this charge is half of the strength of the other charge.

Explanation:

The electric force acting on the charge particle is given by :

F = q E

[tex]E=\dfrac{F}{q}[/tex]

Where

q is the charged particle

E is the electric field

If the magnitude of a charge is twice as much as another charge, q' = 2q, but the force experienced is the same, then the new electric field is given by :

[tex]E'=\dfrac{F}{q'}[/tex]

[tex]E'=\dfrac{F}{(2q)}[/tex]

[tex]E'=\dfrac{1}{2}\times \dfrac{F}{q}[/tex]

[tex]E'=\dfrac{E}{2}[/tex]

So, the new electric field strength of this charge is half of the strength of the other charge. Hence, this is the required solution.

Final answer:

The electric field strength of the charge with twice the magnitude is half the strength of the electric field of the other charge because the force experienced by both is equal.

Explanation:

If the magnitude of a charge is twice as much as another charge, but the force experienced by each is the same, then the electric field strength that the larger charge is in is half the strength of the other charge’s electric field. The electric field strength (E) at a point is defined as the force (F) experienced by a positive test charge (q) placed at that point divided by the magnitude of the charge itself: E = F/q.

If we have two charges, q1 and q2, where q2 is twice q1 (“q2 = 2 × q1”), and the forces on both charges are equal (“F1 = F2”), we can set up the following equations: E1 = F1/q1 and E2 = F2/q2. Combining our known relationships, we get E1 = F/q1 and E2 = F/(2 × q1), which simplifies to E1 = 2 × E2. Therefore, E2 is half the magnitude of E1, meaning that the electric field strength of the charge with twice the magnitude is half the strength of the electric field of the other charge.

A star goes through multiple stages of life represented on the H-R Diagram, from the main sequence stage to a red giant, then a brief stable period after a helium flash, back to a giant, and finally, death. The 'main-sequence turnoff' on the H-R diagram marks where stars begin to leave the main sequence. These stages occur faster for more massive stars.

Stars progress through various stages on the H-R diagram as they age. Initially, in the main sequence stage, stars start by fusing hydrogen in their cores. The most massive stars evolve into red giants and supergiants less than a million years after they reach the main sequence, moving up and to the right on the diagram. After, lower mass stars also begin their departure from the main sequence.

During the next phase of evolution, a star experiences a helium flash which causes a change in its internal structure, leading to a brief period of stability. Following the exhaust of the central helium, the star turns into a giant again and its position on the H-R diagram shifts to high luminosity and low temperature. During the final stage of the star's life, it depletes its inner resources and begins to die.

This process of evolution is faster for more massive stars, as the rate at which they go through each stage of life is higher. The main-sequence turnoff point on the H-R diagram denotes the location where stars begin to leave the main sequence and transform towards the red giant region. It is lower on the H-R diagram and the mass of the stars is lower in older clusters.

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Answer:The answer can be calculated by doing thefollowing steps;

Explanation:

The linear velocity of the 100 g ball in the rotating system with a 130 g ball and a 230 g ball, connected by a rigid rod and rotating at 120 RPM, is approximately [tex]\(4.24 \, \text{m/s}\).[/tex]

Given values:

- Mass of the 130 g ball [tex](\(m_1\))[/tex]: 130 g

- Mass of the 230 g ball [tex](\(m_2\))[/tex]: 230 g

- Length of the rod [tex](\(r\)):[/tex] 34 cm = 0.34 m

- Initial angular velocity [tex](\(ω_{\text{initial}}\))[/tex]: [tex]\( ω_{\text{initial}} = \frac{2π \times 120}{60} \)[/tex]

Now, let's calculate the initial angular velocity:

[tex]\[ ω_{\text{initial}} = \frac{2π \times 120}{60} = 4π \, \text{rad/s} \][/tex]

Next, calculate the moment of inertia for each ball:

[tex]\[ I_1 = \frac{2}{5}m_1r^2 = \frac{2}{5} \times 0.13 \times (0.34)^2 \][/tex]

[tex]\[ I_2 = \frac{2}{5}m_2r^2 = \frac{2}{5} \times 0.23 \times (0.34)^2 \][/tex]

Now, calculate the total moment of inertia:

[tex]\[ I_{\text{total}} = I_1 + I_2 \][/tex]

Substitute the values into the conservation of angular momentum equation:

[tex]\[ I_{\text{total}} \times ω_{\text{initial}} = I_{\text{total}} \times ω_{\text{final}} \][/tex]

Solve for [tex]\(ω_{\text{final}}\)[/tex] and then use it to calculate the linear velocity [tex](\(v\))[/tex] of the 100 g ball:

[tex]\[ v = ω_{\text{final}} \times r \][/tex]

After performing these calculations, we can determine the speed of the 100 g ball. Let me provide you with the numerical results in the next response.

After performing the calculations, the final angular velocity [tex](\(ω_{\text{final}}\))[/tex] is determined to be the same as the initial angular velocity [tex](\(4π \, \text{rad/s}\))[/tex]. Now, we can calculate the linear velocity [tex](\(v\))[/tex] of the 100 g ball using the formula [tex]\(v = ω_{\text{final}} \times r\).[/tex]

[tex]\[ v = 4π \times 0.34 \][/tex]

[tex]\[ v \approx 4 \times 3.14 \times 0.34 \][/tex]

[tex]\[ v \approx 4.24 \, \text{m/s} \][/tex]

Therefore, the speed of the 100 g ball in this rotating system is approximately [tex]\(4.24 \, \text{m/s}\).[/tex]

Answer:

Initial concentration of the reactant = 3.34 × 10^(-2)M

Explanation:

Rate of reaction = 2.30×10−4 M/s,

Time of reaction = 80s

Final concentration = 1.50×10−2 M

Initial concentration = Rate of reaction × Time of reaction + Final concentration

= 2.30×10−4 M/s × 80s + 1.50×10−2 M = 3.34 × 10^(-2)M

Initial concentration = 3.34 × 10^(-2)M

Answer:

20.6m

Explanation:

The mass is useless in this case.  

Kinetic Energy = Potential Energy

g is acceleration due to gravity.

(1/2)mv² = mgh (m's drop out)

(1/2)v² = gh

(1/2)(20.1²) = 9.81(h)

h = (20.1 x 20.1)/9.81 x 2

20.61 meters

Answer:

Tribe historians would: Depict a significant event for each year on a buffalo or deer skin

Tribes of the Sioux Nation maintained historical calendars composed of winter counts, using pictorial representations to record significant events. Winter counts served as a visual record of the tribe's history and were passed down through generations.

Tribes of the Sioux Nation (among other Plains Indians) maintained historical calendars composed of winter counts. Tribe historians would use pictorial representations to record significant events that occurred during each year. Each year, a new pictorial symbol would be added to the count. For example, if a significant battle occurred during a year, the historian would draw a symbol representing that battle. Winter counts served as a visual record of the tribe's history and were often passed down from generation to generation.

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Answer:

[tex]MA=\frac{F_l}{F_e}>1[/tex]

Explanation:

The mechanical advantage with a shorter lever will always be greater than 1.

It is so because with a longer effort arm we need to apply lesser force to lift a unit mass which is at a shorter distance from the fulcrum. This is in accordance with the conservation of moments.

[tex]F_e\times d_e=F_l\times d_l[/tex]

where:

[tex]F_e=[/tex] force on the effort arm

[tex]F_l=[/tex] force on the load arm

[tex]d_e\ \&\ d_l[/tex] are the lengths of load effort arm and load arm respectively.

So, one factor balances the other keeping the product of the two constant.

And we know that mechanical advantage is :

[tex]MA=\frac{F_l}{F_e}[/tex]

Explanation:

The life span of a star is quite as many more than 10 billion years. During these many years it would pass through different stages of its life,  from nebula to ( perhaps, the current stage) supernova to neutron star or Black Hole.

The stages of the life of star over a span of 13 billion year can be summarized as

the transition stages are

Nebula → Blue star → Blue-white super-giant  star → Supernova → Neutron star →Black Hole.

Answer:

Resistance will become 4 times the previous value

Explanation:

We have given current in the circuit i = 2.4 A

According to ohm's law current in the circuit is given by [tex]I=\frac{V}{R}[/tex]

So [tex]2.4=\frac{V}{R}[/tex]............eqn 1

Now voltage is increased to 4 times so new voltage = 4 V

And current in the circuit is same as 2.4 A

We have to fond the resistance so that after increasing voltage current will be same

So [tex]2.4=\frac{4V}{R_{unknown}}[/tex]..........eqn 2

Dividing eqn 1 and 2

[tex]1=\frac{V}{R}\times \frac{R_{unkown}}{4V}[/tex]

[tex]R_{unknown}=4R[/tex]

So resistance will become 4 times the previous value

Answer:

It should increase to four times its value.

Explanation:

Answer:

262 kN/C

Explanation:

If the electrons is moving parallel, thus it has a retiline movement, and because the velocity is varing, it's a retiline variated movement. Thus, the acceleration can be calculated by:

v² = v0² + 2aΔS

Where v0 is the initial velocity (2.0x10⁷ m/s), v is the final velocity (4.0x10⁷ m/s), and ΔS is the distance (1.3 cm = 0.013 m), so:

(4.0x10⁷)² = (2.0x10⁷)² + 2*a*0.013

16x10¹⁴ = 4x10¹⁴ + 0.026a

0.026a = 12x10¹⁴

a = 4.61x10¹⁶ m/s²

The electric force due to the electric field (E) is:

F = Eq

Where q is the charge of the electron (-1.602x10⁻¹⁹C). By Newton's second law:

F = m*a

Where m is the mass, so:

E*q = m*a

The mass of one electrons is 9.1x10⁻³¹ kg, thus, the module of electric field strenght (without the minus signal of the electron charge) is:

E*(1.602x10⁻¹⁹) = 9.1x10⁻³¹ * 4.61x10¹⁶

E = 261,866.42 N/C

E = 262 kN/C

Answer: b. PREVALENCE

Explanation:

Prevalence can be defined as the proportion of individuals in a population having a disease or common characteristic. Prevalence of a particular disease is number of people in a population who have develop a disease at a particular time.

It can be expressed in form of proportion Which equals the number of developed cases at a particular time divided by the total number of population.

The balloon accelerated because of Newton's third law of motion. When the air in the balloon is forcefully ejected, the balloon experiences an equal and opposite force, causing it to accelerate in the opposite direction.

The acceleration of the balloon when it slips from Miko's hand is due to Newtons third law of motion. This law states that for every action, there is an equal and opposite reaction. In this case, when the air is forcefully ejected or escapes from the balloon, the balloon experiences an equal and opposite force which causes it to shoot off or accelerate in the opposite direction of the escaping air. This is the same principle that explains the propulsion of rockets and the recoil of guns.

You can visualize the movement of the balloon somewhat like the exploding fireworks shown in figure 9.31. The fireworks explode and eject matter in all directions - and its center of mass behaves similarly to the balloon's - accelerated by the ejection of matter. The balloon, like the firework, would keep the parabolic path of flight as long as there was matter (or in the balloon's case, air) pushing it forward. Once all of the air has escaped, the balloon starts to fall due to gravity, like any other free-falling object.

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Answer:

b. fluid friction occurs

Explanation:

Water is a liquid and both going through air gas and liquid cause fluid friction.

Answer:

The moment of inertia about the rotation axis is 145.35 kg.m²

Explanation:

Given:

Mass of each seat = 6.4 kg

length of rods attached to the seat = radius of the seat from center = 1.5m

Moment of inertia = M₁r²

Moment of inertia about the first child:

total mass at that point = mass of the child + mass of the seat

                                      = 16kg + 6.4 kg = 22.4 kg

Moment of inertia at the point where the first child sits = 22.4 *1.5²

= 50.4 kg.m²

Moment of inertia about the second child:

total mass at that point = mass of the child + mass of the seat

                                       = 23kg + 6.4 kg = 29.4 kg

Moment of inertia at the point where the second child sits = 29.4 *1.5²

= 66.15 kg.m²

Moment of inertia about the two empty seats:

Moment of inertia about the two seats = 2(6.4*1.5²)

= 28.8 kg.m²

Moment of inertia about the rotation axis = Moment of inertia about the point of two children + moment of inertia about the two seat

= (50.4 + 66.15 + 28.8) kg.m²

= 145.35 kg.m²

Therefore, the moment of inertia about the rotation axis is 145.35 kg.m²

The moment of inertia about the rotation axis is 145.35 kgm2.

Given that the mass m_s of the seat is 6.4 kg, length r of the rod is 1.5 m. The masses of two children is m1 = 16 kg and m2 = 23 kg.

The moment of inertia about the first child is calculated given below.

[tex]MI _1 = (m_s+m_1)r^2[/tex]

[tex]MI_1 = (6.4+16)\times 1.5^2[/tex]

[tex]MI_1 = 50.4 \;\rm kg m^2[/tex]

The moment of inertia about the second child is calculated given below.

[tex]MI _2= (m_s+m_2)r^2[/tex]

[tex]MI_2 = (6.4+23)\times 1.5^2[/tex]

[tex]MI_2 = 66.15 \;\rm kg m^2[/tex]

The moment of inertia about the two empty seats is calculated given below.

[tex]MI_s = 2(m_sr^2)[/tex]

[tex]MI_s = 2 ( 6.4\times 1.5^2)[/tex]

[tex]MI_s = 28.8 \;\rm kgm^2[/tex]

The moment of inertia about the rotation axis is the total sum of the moment of inertia about the point of two children and the moment of inertia about the two seats.

[tex]MI = MI_1 +MI_2+MI_s[/tex]

[tex]MI = 50.4 + 66.15 + 28.8[/tex]

[tex]MI = 145.35 \;\rm kgm^2[/tex]

Therefore, the moment of inertia about the rotation axis is 145.35 kgm2.

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Answer:

410.254 N

Explanation:

Force: This can be defined as the product of the mass of a body. The Unit of force is Newton (N)

Deduced from the question,

Force applied to the box to start it moving = Force of friction.

Fₐ = F

Where Fₐ = Force applied to the box to start it moving, F = Force of friction.

But,

F = μR.......................... Equation 1

Where R = normal reaction, μ = coefficient of static friction.

R = W =  mg ( on a level surface)

Where m = mass of the box = 123 kg, g = acceleration due to gravity = 9.81 m/s²

R = 123×9.81

R = 1206.63 N.

Also, μ = 0.34

Substituting into equation 1

F = 1206.63×0.34

F = 410.254 N.

Thus the force applied to the box to start it moving = 410.254 N

Answer:

The sentence is following with "are made from mostly silicon material".

Explanation:

Silicon is extracted and refined by the use of electrical energy. The amount of energy required to produce the silicon in a solar cell is greater than the energy that cell will produce during its useful working life.

Answer:

C

Explanation:

The answer is polarization. In a normal molecule the positive and negative charges are distributed in a way that it makes a continuous distribution with no net force. but when you apply an external electric force, the opposite charges go to the opposite ends of the molecule making them a polarized molecule.

This is called polarization.

I hope it helps you.

Thank you.  

Answer:

southwest

Explanation:

Here, all the particles have same charge this means that only repulsive force is acting on the particles according to Coulomb's laws.

One particle is 1 m to my north and another particle is to my east.

The particle to my north will push the positive charge I am holding to the south and the particle to my east will push the positive charge I am holding to the west.

Hence, the resultant direction of the force will be southwest.

Answer:

c. the tilt of the axis of rotation with respect to the Plane of the Ecliptic

Explanation:

The inclination of the ecliptic (or known only as obliqueness) refers to the angle of the axis of rotation with respect to a perpendicular to the plane of the eclipse. He is responsible for the seasons of the year that the planet Earth lends. It is not constant but changes through the movement of nutation. The terrestrial plane of Ecuador and the ecliptic intersect in a line that has an end at the point of Aries and at the diametrically opposite point of Libra.

When the Sun crosses the Aries, the spring equation occurs (between March 20 and 21, the beginning of spring in the northern hemisphere and the early autumn of the southern hemisphere), and from which the Sun is in the North Hemisphere; Pound until you reach the point of the autumn equinox (around September 22-23, beginning fall in the northern hemisphere and spring in the southern hemisphere).

Answer:

a) 31.02 m/s

b) - 653.24 m/s²

c) 50 ms

Explanation:

a) For a vertical movement, let's suppose that the woman fell by the rest, thus she's initial velocity v0 = 0 m/s. If she makes a distance (S) of 161 ft = 49.1 m, thus, her final velocity at the box, v is:

v² = v0² +2aS

The acceleration is the gravity acceleration, 9.8 m/s².

v² = 2*9.8*49.1

v² = 962.36

v =√962.36

v = 31.02 m/s

b) She crushes the box until she stops, so her final velocity will be 0 m/s. The initial velocity is now 31.02 m/s, and S = 29 in = 0.7366 m

0 = 31.02² + 2a*0.7366

-1.4732a = 962.36

a = - 653.24 m/s² (the negative signal indicates that she's dessacelaranting)

c) The time can be calculate by:

v = v0 + at

0 = 31.02 -653.24*t

653.24t = 31.02

t = 0.05 s = 50 ms

Answer:

Velocity of rocket will be equal to 7.81 m/sec

Explanation:

We have given mass of the rocket [tex]m_1=4kg[/tex]

Mass of fuel is given [tex]m_2=50gram=0.05kg[/tex] ( As 1 kg is equal to 1000 gram )

Velocity of fuel [tex]v_2[/tex] = 625 m/sec

We have to find the velocity of rocket [tex]v_1[/tex]

From conservation of momentum we know that initial momentum is equal to final momentum '

So [tex]m_1v_1=m_2v_2[/tex], here [tex]m_1[/tex] is mass of rocket [tex]v_1[/tex] is velocity of rocket [tex]m_2[/tex] is mass of fuel and [tex]v_2[/tex] is velocity of fuel

So [tex]4\times v_1=625\times 0.05[/tex]

[tex]v_1=7.81m/sec[/tex]

So velocity of rocket will be equal to 7.81 m/sec

Answer: Jane 6ft from fulcrum

John 4 ft from fulcrum

Explanation: You use the law of moment of force.

That is Clockwise moment equals anti clockwise moment.

Here is the attachment involving the diagram and procedure of calculations and the answers.

The small child should sit 1.30 m away from the pivot point on the seesaw to maintain balance.

The small child should sit 1.30 m away from the pivot point on the seesaw to maintain balance.

Answer:

[tex]331665750000\ m/s^2[/tex]

3257806.62409 m/s

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

M = Mass of Sun = [tex]1.989\times 10^{30}\ kg[/tex]

r = Radius of Star = 20 km

u = Initial velocity = 0

v = Final velocity

s = Displacement = 16 m

a = Acceleration

Gravitational acceleration is given by

[tex]g=\dfrac{GM}{r^2}\\\Rightarrow g=\dfrac{6.67\times 10^{-11}\times 1.989\times 10^{30}}{20000^2}\\\Rightarrow g=331665750000\ m/s^2[/tex]

The gravitational acceleration at the surface of such a star is [tex]331665750000\ m/s^2[/tex]

[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 331665750000\times 16+0^2}\\\Rightarrow v=3257806.62409\ m/s[/tex]

The velocity of the object would be 3257806.62409 m/s

(a) the acceleration due to gravity is 3.3 × 10¹¹ m/s²

(b) the final velocity of the object is 3.26 × 10⁶ m/s

Given that the neutron star has a mass equal to Sun, M = 2 × 10³⁰ kg

Radius of the star is R = 20 km = 20 × 10³

The weight on the surface of a neutron star that has the same mass as our Sun and a diameter of 21.0 km will be 8.29 × 10¹³ N

(a) The gravitational force on the surface of the neutron star is given by:

F = GMm/R²

mg = GMm/R²

where G is the gravitational constant

M is the mass of the body

m is the mass of the person

and, R is the radius of the body

So,

g = GM/R²

g = (6.67 × 10⁻¹¹)( 2 × 10³⁰)/ (210 × 10³)²

g = 3.3 × 10¹¹ m/s²

(b) According to the third equation of motion:

v² = u² + 2gh

v² = 2gh , since u = 0 as the object is at rest initially

v = [tex]\sqrt{2\times3.3\times10^{11}\times16}[/tex]

v = 3.26 × 10⁶ m/s

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The initial horizontal velocity of the soccer ball is 16.5 m/s

Explanation:

When we throw a ball, there is a constant velocity horizontal motion and there is an accelerated vertical motion. These components act independently of each other.  Horizontal motion is constant velocity motion.

            [tex]v_{x f}=v_{x i}=v_{x}[/tex]

[tex]a_{x}=0[/tex], so [tex]x=v_{i x} t+\left(\frac{1}{2}\right) a_{x} t^{2}[/tex] for horizontal motion

[tex]y=v_{i y} t+\left(\frac{1}{2}\right) a_{y} t^{2}[/tex] for vertical motion

Given:

x = 35 m

[tex]a_{x}=0 \mathrm{m} / \mathrm{s}^{2}[/tex]

Need to find [tex]v_{i x}[/tex]

y = - 22 m

[tex]v_{i y}=0 \mathrm{m} / \mathrm{s}[/tex]

[tex]a_{y}=-9.8 \mathrm{m} / \mathrm{s}^{2}[/tex]  (negative sign indicates downward motion)

By substituting all known values, we can solve for 't' value as below

[tex]y=v_{i y} t+\left(\frac{1}{2}\right) a_{y} t^{2}[/tex]

[tex]-22=0(t)+\left(0.5 \times-9.8 \times t^{2}\right)[/tex]

[tex]t^{2}=\frac{-22}{0.5 \times-9.8}=\frac{-22}{-4.9}=4.4897[/tex]

Taking square root, we get  t = 2.12 seconds

Now, substitute these to find initial horizontal velocity

[tex]x=v_{i x} t+\left(\frac{1}{2}\right) a_{x} t^{2}[/tex]

[tex]35=v_{i x}(2.12)+\left(0.5 \times 0 \times(2.12)^{2}\right)[/tex]

[tex]35=v_{i x}(2.12)+0[/tex]

[tex]v_{i x}=\frac{35}{2.12}=16.5 \mathrm{m} / \mathrm{s}[/tex]