how to calculate the maximum height of a projectile given its original position and initial velocity only up and down

The net force on each car is zero, and both cars will continue to move at their constant speeds without any acceleration or change in direction.

According to Newton's third law of motion, every action has an equal and opposite reaction.

Let's calculate the magnitude of the force exerted by car A on car B and vice versa:

The force (F) is given by the formula:

[tex]F = m * a[/tex]

where m is the mass of the car and a is the acceleration it experiences.

When the two cars pass each other, the acceleration of each car is zero because their speeds are constant. Therefore, the net force on each car is zero, and the force exerted by car A on car B is equal in magnitude and opposite in direction to the force exerted by car B on car A.

The force exerted by car A on car B is:

[tex]F_{AB} = m_A * a_A[/tex]

where [tex]m_A = 500 kg[/tex] and [tex]a_A = 0 m/s^2[/tex] (constant speed)

[tex]F_{AB} = 500 kg * 0 m/s^2 = 0 N[/tex]

Similarly, the force exerted by car B on car A is:

[tex]F_{BA} = m_B *a_B[/tex]

where [tex]m_B = 800 kg[/tex] and [tex]a_B = 0 m/s^2[/tex] (constant speed)

[tex]F_{BA} = 800 kg * 0 m/s^2 = 0 N[/tex]

As we can see, both forces are zero. Therefore, the net force on each car is zero, and both cars will continue to move at their constant speeds without any acceleration or change in direction.

Learn more about acceleration :

https://brainly.com/question/12550364

#SPJ4

The direction and intensity of the electric field close to the charged particles would be indicated by the electric field lines.

It has been determined that a charged particle is one that possesses an electric charge. The atom at the atomic level is made up of a nucleus that the electrons orbit. The proton charge, which is 1.602 1019 Coulombs, is what gives the nucleus its positive charge because it is made up of neutrons and protons.

The ability to conduct electricity is a characteristic of many fundamental, or subatomic, components of matter. As an illustration, protons and neutrons both have positive charges but electrons have a negative charge.

To know more about charged particles visit:-

https://brainly.com/question/18750504

#SPJ1

An example of electrical energy being transformed into thermal energy is an iron plugged into an outlet. The correct option is B.

The type of energy that is existing in a group that finds its temperature is mentioned to as thermal energy. Thermal energy flows as heat. Energies always transfer from one form to another form when some work done.

When iron is plugged in, it gets electrical energy and the energy gets converted into thermal energy and iron gives heat.

Therefore, the correct option is B. an iron plugged into an outlet.

To learn more about thermal energy, refer to the link:

https://brainly.com/question/3022807

#SPJ9

The electric field strength between the two plates of the parallel-plate capacitor is 2.135e4 V/m.

The electric field strength between the plates of a parallel-plate capacitor is given by:

E = V/d

where E is the electric field strength, V is the potential difference between the plates, and d is the separation between the plates.

In this case, the potential difference between the plates is 2.85 V, and the separation between the plates is 1.33e-4 m. Plugging these values into the formula, we get:

E = 2.85 V / 1.33e-4 m

= 2.135e4 V/m

Therefore, the electric field strength between the two plates of the parallel-plate capacitor is 2.135e4 V/m.

Learn more about parallel-plate capacitor here :

brainly.com/question/12733413

#SPJ4

If we replaced the three resistors with a single resistor,  the resistance req of this resistor is  R1​+R2​+R3.For the series combination of resistances, here the second end of each resistance is attached to the first end  of the following resistance and the setting goes  so on

In a series circuit of resistors, the current that runs through every one of them is identical and is equivalent to the current provided by the battery. Since the resistances are distinct and the same current flows through each one, the potential difference  between the different resistors will be different.

let the three resistors R1, R2, and R3 are arranged in a series circuit with a  battery providing a potential difference V. The current I supplied  by  the battery to this combination is then shared between the three resistors.Consider V1, V2 and V3 be the  potential difference acrross resistance  R1,R2,R3 ends V=V1​+V2​+V3​   ........(1).

Considering the replaced  resistance be R,  by ohm's law V=IR,V1​=IR1​,V2​=IR2​,V3​=IR3​, so substituing those in equation 1 we get :

I=IR1​+IR2​+IR3​

IR=I(R1​+R2​+R3​)

R=R1​+R2​+R3​

In conclusion, the replaced resistor resistance  is the sum of the individual  resistances

To know more about ohm's law refer to the link  brainly.com/question/1247379

#SPJ4

Answer:

Explanation:

The gravitational force between two objects can be calculated using the formula:

F = G * (m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 is the mass of one object (60 kg), m2 is the mass of the other object (5.67 x 10^26 kg), and r is the distance between the two objects (the radius of Saturn, 6.3 x 10^7 m).

F = 6.67 x 10^-11 * (60 * 5.67 x 10^26) / (6.3 x 10^7)^2

F = 6.67 x 10^-11 * 3.402 x 10^33 / 3.969 x 10^14

F = 2.30 x 10^19 N

So the gravitational force on a 60 kg man on Saturn would be approximately 2.30 x 10^19 N.

The complex dance of gravity between celestial objects is what gives rise to the structures we see in the universe, from planets orbiting stars to galaxies forming clusters.

Gravity is the force that governs the movement of celestial bodies in the universe, including planets around the sun, stars grouped in galaxies, and galaxies grouped in clusters.

For example, the gravity of the sun keeps the planets in orbit around it. The planets are constantly pulled towards the sun by gravity, but they are also moving tangentially to the sun at high speeds. The combination of these two forces creates a balanced system, where the gravitational pull of the sun keeps the planets in their orbits around it.

Similarly, the gravity between stars in galaxies and galaxies in clusters acts as a binding force, keeping them together despite the vast distances between them.

To know more about the gravity, here

brainly.com/question/21454806

#SPJ4

Your perceived weight is equal to the normal force. Therefore, when the elevator accelerates upward or downward, you truly feel a little heavier than usual and a little lighter than usual.

(a) The normal force on you is larger than your weight when the elevator is moving down and coming to a stop. This is because the normal force is the force that the floor exerts on you in order to prevent you from falling downwards, and the acceleration of the elevator is greater than the acceleration of gravity.

(b) The normal force on you is equal to your weight when the elevator is moving up and coming to a stop. This is because the acceleration of the elevator and the acceleration of gravity are the same, so the normal force is equal to the force of gravity.

(c) The normal force on you is larger than your weight when the elevator is moving up and speeding up. This is because the acceleration of the elevator is greater than the acceleration of gravity, so the normal force is greater than the force of gravity.

(d) The normal force on you is equal to your weight when the elevator is moving down at constant speed. This is because the acceleration of the elevator is equal to the acceleration of gravity, so the normal force is equal to the force of gravity.

To learn more about normal force click here https://brainly.com/question/13340671

#SPJ4

The velocity of the target ball after the collision is 2.4 m/sec.

We can use the conservation of momentum and the conservation of kinetic energy to solve this problem.

Let's define the following variables:

m1 = mass of incoming softball = 0.220 kg

u1 = initial velocity of incoming softball = 5.5 m/s

v1 = final velocity of incoming softball after collision = -3.1 m/s

m2 = mass of target ball

v2 = final velocity of target ball after collision

By the conservation of momentum, we have:

[tex]m_1 u_1 + 0 = m_1 v_1 + m_2 v_2[/tex]

Simplifying this equation, we get:

[tex]m_2 v_2 = m_1 * (u_1 - v_1)[/tex]

[tex]m_2 v_2 = 0.220 * (5.5 - (-3.9))[/tex]

[tex]m_2 v_2 = 0.220 * (5.5 +3.9))[/tex]

[tex]m_2 v_2 = 0.220 * (9.4)[/tex]

[tex]m_2 v_2 = 2.068[/tex] ..... eq(i)

The approach velocity is equal to the separation velocity, therefore,

[tex]u_1 - u_2 = v_2 -v_1[/tex]

[tex]5.5 = v_2 -(-3.1)[/tex]

[tex]5.5 = v_2 +3.1[/tex]

v2 = 2.4

Now, eq(i) becomes,

m2 * 2.4 = 2.068

m2 = 0.862

Read more about Collision:

https://brainly.com/question/13004146

#SPJ4

This extra current is used by the op amp to boost the input signal and drive the output. The current supplied by the op amp can be slightly less than the current drawn from the power supply.

Although some parts can manage closer to 100 mA and others will struggle to provide you with 10 mA, a typical op-amp can be expected to consistently sink or source not more than 30 or 40 mA.

Op-amps require a DC supply voltage, which can range in range from a few volts to at least 30 volts. If the power supply is a perfect DC voltage source, which means it consistently outputs the same voltage. The only factors influencing the op-output amp's are its inputs.

To know more about current visit:-

https://brainly.com/question/23323183

#SPJ1

Speed = 92.6 km/2.9 hours = 32.0 km/h

x-component of velocity = 32.0 km/h * cos(29.3 degrees) = 29.4 km/h

y-component of velocity = 32.0 km/h * sin(29.3 degrees) = 16.0 km/h

Velocity components are vector quantities that describe the direction and magnitude of an object's motion. The total velocity of an object can be determined by adding the components that make up its total velocity. These components are often referred to as x-velocity and y-velocity, which represent the speed of the object in a certain direction. The magnitude of these components is determined by the speed of the object and the angle it is traveling at. The two components of velocity can be combined to calculate the total velocity of an object.

Distance = 92.6 km

Time = 2.9 h

To calculate the velocity, divide the distance by the time:

velocity = 92.6/2.9 = 32 km/h

To calculate the x component of the velocity, use trigonometry:

vx = 32cos(29.3) = 29.4 km/h

To calculate the y component of the velocity,use trigonometry:

vy = 32sin(29.3) = 16.8 km/h

Therefore, the bird's velocity is 29.4 km/h in the x direction and 16.8 km/h in the y direction.

To know more about Velocity component, visit:

https://brainly.com/question/24681896

#SPJ4

The displacement of the train to the west is 478 km.

To find the displacement to the west, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the straight-line distance from the starting point to the ending point) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the displacement to the west "x". Then, the displacement to the south is 42 km, and the total displacement (the distance traveled by the train) is 478 km. Using the Pythagorean theorem, we can write the following equation:

x^2 + 42^2 = 478^2

Expanding the squares:

x^2 + 42^2 = 478^2

x^2 + 1764 = 229284

x^2 = 227620

x = 478 km

Learn more about displacement here: https://brainly.com/question/2109763

#SPJ1

The opposite side of earth will experience one on the side facing the Moon (high tide) and the other on the opposite side of the Earth (low tide).

If the side of the Earth that faces the Moon experiences a tidal bulge, it is due to the gravitational pull of the Moon on the water on the surface of the Earth. This gravitational pull causes the water to bulge out on the side of the Earth facing the Moon, resulting in a high tide. On the opposite side of the Earth, however, the gravitational pull of the Moon is weaker because it is farther away. As a result, the water on this side of the Earth is not pulled as strongly by the Moon's gravity and is left with a lower gravitational potential energy. This results in a second bulge, which is caused by the centrifugal force of the Earth's rotation. So, the opposite side of the Earth will also experience a tidal bulge, but it will be a low tide because the water is being pulled away from the Earth due to the weaker gravitational pull of the Moon. Therefore, there are two tidal bulges on the Earth, one on the side facing the Moon (high tide) and the other on the opposite side of the Earth (low tide). The areas in between these two bulges experience moderate tides. These tidal bulges and their movements are responsible for the daily tidal patterns that we observe on Earth.

To know more about Earth please refer: https://brainly.com/question/367736?referrer

#SPJ4

If Bill's ball reaches a maximum height of h, then Joe's ball will reach a maximum height of 2h.

Assuming that air resistance is negligible, the maximum height of a ball thrown vertically upwards is given by the formula:

[tex]h = (v^2)/(2g)[/tex]

where h is the maximum height, v is the initial Speed, and g is the acceleration due to gravity.

Let's assume that Bill throws the ball with an initial velocity v, and Joe throws his ball with an initial velocity 2v.

Then, the maximum height of Bill's ball is:

[tex]h = (v^2)/(2g)[/tex]

And the maximum height of Joe's ball is:

[tex]h = ((2v)^2)/(2g) = (4v^2)/(2g) = 2(v^2)/(g)[/tex]

So the maximum height of Joe's ball is twice the maximum height of Bill's ball.

To know more about Speed/Velocity, here

https://brainly.com/question/22610586

#SPJ4

(a) The initial position of the stone is at the edge of the cliff, so the x-coordinate is 0 and the y-coordinate is the height of the cliff, h = 50.0 m.

(b) The stone is thrown horizontally, so the initial velocity in the x-direction, vx, is 18.0 m/s and the initial velocity in the y-direction, vy, is 0 m/s.

(c) The appropriate analysis model for the vertical motion of the stone is projectile motion under constant acceleration due to gravity.

(d) The appropriate analysis model for the horizontal motion of the stone is uniform motion with constant velocity.

(e) The equations for the x and y components of the velocity of the stone as a function of time can be written as: vx = 18.0 m/s (constant)

vy = -gt (where g is the acceleration due to gravity, and t is time)

(f) The equations for the position of the stone as a function of time can be written as: x = vx t, y = h + vy t - 1/2 g t^2

(g) The stone strikes the water below the cliff after about 3.19 seconds.

(h) The stone lands with a speed of about 30.0 m/s and an angle of impact of about 26.5 degrees below the horizontal.

(g) To find the time it takes for the stone to strike the water below the cliff, we need to find the time at which y = 0.

Substituting y = 0 and h = 50.0 m into the equation for y, we get:

0 = 50.0 m - 1/2 g t^2

t = sqrt(2h/g)

= [tex]\sqrt{(2*50.0 m/9.81 m/s^2)[/tex] ≈ 3.19 s

(h) To find the speed and angle of impact,

we need to find the final velocity of the stone just before it hits the water.

The final velocity can be found using the equation:

v^2 = vx^2 + vy^2 + 2gy

Substituting the values we know, we get:

[tex]v^2 = (18.0 m/s)^2 + (-9.81 m/s^2)(3.19 s)^2 + 2(9.81 m/s^2)(50.0 m)[/tex]

v ≈ 30.0 m/s

The angle of impact can be found using the equation:

tan(theta) = vy/vx

Substituting the values we know, we get:

[tex]theta = tan^-1(vy/vx) = tan^-1\frac{(\frac{(-9.81 m/s^2)}{(3.19 s)}}{18.0} m/s)[/tex]

≈ -26.5 degrees

For more questions on Angle of Impact

https://brainly.com/question/12262372

#SPJ4

False. The unit used to measure the energy contained in natural gas is typically joules or cubic meters (m^3) of natural gas. The term "therm" is sometimes used as a unit of energy, but it is more commonly used to describe the amount of energy contained in 100,000 British thermal units (BTUs). In the United States, the therm is sometimes used to describe the amount of energy contained in 100 cubic feet of natural gas.

To calculate the final change in the system's internal energy, we need to consider the work done by the external force and the work done by friction.

The work done by the external force can be calculated using the formula:

W_ext = F_ext * d

Where W_ext is the work done by the external force, F_ext is the external force, and d is the distance traveled by the block.

Since the block comes to a complete stop, the work done by the external force is equal to the work done by friction, which can be calculated using the formula:

W_friction = F_friction * d = μ_k * m * g * d

Where W_friction is the work done by friction, F_friction is the frictional force, μ_k is the coefficient of kinetic friction, m is the mass of the block, g is the acceleration due to gravity, and d is the distance traveled by the block.

W_ext = ΔK. Where ΔK is the change in the kinetic energy of the block, which can be calculated using the formula: ΔK = (1/2) * m * v_f^2 - (1/2) * m * v_i^2. Where v_f is the final velocity of the block, and v_i is the initial velocity of the block. Since the block comes to a complete stop, the final velocity of the block is 0 m/s. Therefore, we can simplify the equation for ΔK:

ΔK = (1/2) * m * v_i^2. Substituting the values given in the problem statement, we get: ΔK = (1/2) * 1.6 kg * (2.4 m/s)^2 = 6.912 J

Now, we can equate the work done by the external force and the work done by friction:

W_ext = W_friction

ΔK = μ_k * m * g * d

Solving for d, we get:

d = ΔK / (μ_k * m * g) = 6.912 J / (0.03 * 1.6 kg * 9.81 m/s^2) ≈ 14.05 m

The work done by friction can be calculated as:W_friction = μ_k * m * g * d ≈ 6.912 J. Therefore, the final change in the system's internal energy is ΔU = -W_friction = -6.912 J. The negative sign indicates that the internal energy of the system has decreased as a result of the work done by friction.

To learn more about external force, visit here

https://brainly.com/question/16186958

#SPJ4

The detailed answer of this question is given below:

The furnace is an  internal                  combustion engine.

A furnace is typically considered an internal combustion engine, although it operates differently than many other types of internal combustion engines.

In a furnace, fuel is burned within a combustion chamber, which generates heat that is then used to heat air or water, depending on the type of furnace. This combustion process is similar to that of internal combustion engines, in which fuel is burned inside a combustion chamber to generate heat and power.

However, unlike many internal combustion engines, a furnace does not typically use pistons, cylinders, or other similar components to convert heat into mechanical energy. Instead, the heat generated by the combustion process is typically used directly, either to heat air or water or to provide heat for other processes.

To know more about Combustion Engine visit:

https://brainly.com/question/16579482

#SPJ4

The statement that is correct about the scenario is

C) From the moment of release to the moment it hits the ground, the system's total mechanical energy, which just contains the block, grows.

D) The block-Earth system's overall mechanical energy stays constant.

It also goes by the name ramp. Objects placed on an inclined plane will slide down the surface with acceleration due to the uneven force acting on it.

Think of a ball rolling at an angle on an inclined surface without friction. Such a ball will be affected by the gravitational force and the normal force, two independent forces.

Therefore, the correct options are C and D.

To learn more about the inclined plane, refer to the link:

https://brainly.com/question/29629164

#SPJ9

Junita will do more work on the square box. when Junita lifts an object to a shelf, she does work on the object, which increases its gravitational potential energy (GPE).

The amount of work done on an object is equal to the increase in its GPE.

Junita lifted a round box and a square box to a shelf. She did work on the boxes, increasing their GPE. The round box's GPE increased by 50 J, meaning Junita exerted 50 J of work.

The square box's GPE increased by 100 J, meaning Junita did 100 J of work on it.

To learn more about gravitational potential energy:

https://brainly.com/question/3120930

#SPJ4

To find the time it will take to travel a certain distance at a certain speed, you can use the formula:

time = distance/speed

In this case, the distance is 90km and the speed is 30km/m.

So, time = 90km / 30km/m = 3m

Answer:

It will take 3 hours to get to the island 90km from the coast in a boat that travels 30km/m.

Answer:

The value of Time Will be

[tex]9minutes[/tex]

Explanation:

Greetings!!!

Distance (s)= 90km

Speed(V)= 30km/m

Time(t)= ?

But before that how did I know Time is required

So, from the given word problem it says "How long will it take" which means it's indicating the time period.

Firstly, recall speed-distance equation

Substitute known variables into the equation

Solve for time

divide both sides of the equation by 30km/m

[tex] \frac{30km/m(t)}{30km/m} = \frac{90km}{30km/m} [/tex]

divide

[tex]t = 3m[/tex]

If you have any questions tag me on comments.

Hope it helps!!!

The expression for dividing distance by speed using floating point arithmetic is float(distance) / (speed).

Arithmetic is the branch of mathematics that deals with the study of numbers, operations such as addition, subtraction, multiplication and division, and the properties of these operations. It is a fundamental component of mathematics, and it is essential for solving problems in everyday life. Arithmetic is used to calculate the cost of goods, to figure out measurements, to estimate taxes, and to perform many other calculations. Arithmetic is an important part of higher-level mathematics, such as calculus, and is often used to solve complex problems.

This expression produces a fractional result by using the float() function, which calculates a floating point value from the given argument (in this case, the integer value of distance). To apply this expression to different variables, simply replace distance and speed with the other variables (e.g. float(children) / (families)).

To learn more about arithmetic
https://brainly.com/question/77702
#SPJ1

Final velocity - Velocity displacement

       Δv            a

2)    -12 m/s        -3 m/s2

3)     5 m/s        2.5 m/s2

What is the final and initial velocity?

1. Final velocity is the speed at which an object is moving at the end of its motion.

2. Initial velocity is the speed at which an object is moving at the beginning of its motion.

3. Final velocity can be determined by subtracting the initial velocity from the total displacement of the object.

4. Initial velocity can be determined by subtracting the total displacement of the object from the final velocity.

2) 0-12 = -12/4 = -3

3) 8-3 = 5/2 = 2.5

4) 46.4-27.3 = 19.1/11 = 1.73

5) 5-15 = -10/5 = -2

Therefore, the above one is the answer for this chart.

To learn more about final and initial velocity from the link

brainly.com/question/9365999

#SPJ1

Answer:

Explanation:

Q=278*126.85*900=31,737,870J

In a 1H NMR spectrum, different signals represent different types of hydrogen atoms. Hydrogen atoms in different chemical environments will have different resonant frequencies due to the local magnetic field they experience.

However, it is possible for hydrogen atoms in the same chemical environment to give the same signal. This occurs when they are in identical chemical environments and experience the same local magnetic field. In this case, they will have the same resonant frequency and contribute to the same peak or signal in the NMR spectrum. These hydrogen atoms are said to be chemically equivalent.

It is important to note that chemically equivalent hydrogen atoms do not have to be in the same molecule. For example, in a mixture of two different molecules with the same chemical environment, the hydrogen atoms in both molecules will contribute to the same NMR signal.

To know more about frequency here

https://brainly.com/question/254161

#SPJ4

Theoretical centre to centre distance will be 3.25 inch or 82.55 mm and Gear tooth = 35.

Circular pitch will remain same

P_c = [tex]\pi[/tex]D_p / Tp =  [tex]\pi[/tex]D_G / T_G

D_p / Tp =  D_G / T_G

T_G = D_G x T_p / D_p = 4.375  / 2.125 x 17

T_G = 35

Center-To-Center distance = pitch circle radius of prism + pitch circle radius of gear

= D_p / 2 +D_G / 2

= 1/2 (2.125 + 4.375)

= 3.25 inch

= 3.25 x 25.4 mm

= 82.55mm

Distance is a measure of the amount of space between two points. It is a fundamental concept in physics and geometry, and is used to describe the length or magnitude of a displacement, movement, or separation. Distance can be measured in different units, such as meters, kilometers, miles, or light years, depending on the scale and context of the measurement.

Distance is a relative concept, as it depends on the reference point or frame of reference. It is also influenced by factors such as time, direction, and velocity, which affect the actual distance traveled or the perceived distance. Thus, distance is a versatile and dynamic concept that plays a crucial role in various fields of knowledge and application.

To learn more about Distance visit here:

brainly.com/question/13034462

#SPJ4

Force in each cord for equilibrium is T_A = 42.2 N, T_B = 20.0 N, T_C = 10.0 N, T_D = 6.7 N, and T_E = 5.0 N.

The force in each cord supporting a 30-kg pipe, we can apply the principles of static equilibrium. Static equilibrium occurs when the net force and net torque on an object are both zero.

In this case, the pipe is being supported by five cords. Let's label the cords A, B, C, D, and E. Since the pipe is not accelerating, the net force on the pipe must be zero. This means that the total upward force provided by the cords must balance the downward force of the weight of the pipe.

To calculate the force in each cord, we can use the principle of the conservation of momentum. Assuming the pipe is stationary, we know that the momentum of the system is constant, and we can apply the principle of moments to determine the tension in each cord. We can take moments about point A, where cord A is attached.

Let T_A, T_B, T_C, T_D, and T_E be the tension forces in cords A, B, C, D, and E, respectively. By taking moments about point A, we have:

T_B * 3 + T_C * 6 + T_D * 9 + T_E * 12 = 30 * g * 3

where g : acceleration due to gravity. Since the pipe is in equilibrium, the sum of the tension forces in the cords must also be equal to the weight of the pipe, or:

T_A + T_B + T_C + T_D + T_E = 30 * g

We now have two equations and two unknowns, T_A and T_B. Solving these equations simultaneously, we obtain:

T_A = 42.2 N

T_B = 20.0 N

T_C = 10.0 N

T_D = 6.7 N

T_E = 5.0 N

Learn more about force here:

https://brainly.com/question/30683294

#SPJ4

The work performed by Zorg between t = 0 and t = T is equal to the product of the constant coefficient b^3 and the time interval T.

The work performed by Zorg can be calculated as the integral of power with respect to time. If Zorg's power output is given by P = b^3, then the work performed by Zorg between time t = 0 and t = T can be calculated as:

W = ∫_0^T P(t) dt = ∫_0^T b^3 dt = b^3 * t |_0^T = b^3 * T

So, the work performed by Zorg between t = 0 and t = T is equal to the product of the constant coefficient b^3 and the time interval T.

learn more about work done: https://brainly.com/question/25573309

#SPJ1

It would have been easier due to Parallax.

If the stars were much closer than they really are, it would have been easier for Aristarchus to persuade people that the Earth moves around the Sun because the concept of parallax would be more noticeable.

Parallax is the apparent shift in the position of an object when viewed from different angles, and it is easier to observe when the objects are closer.

Aristarchus used parallax to support his idea of heliocentrism, but the lack of equipment and knowledge at the time made it difficult for people to comprehend the concept.

However, if the stars were closer, their parallax would be more evident, and people would be more likely to accept the idea that the Earth moves around the Sun. This could have led to an earlier acceptance of the heliocentric model of the solar system.

To know more about parallax visit:

https://brainly.com/question/29210252

#SPJ1

As the length of the string attached to the pendulum increases, its frequency decreases. Hence, the frequency of shorter string will be higher. The frequency of the string is 0.13 Hz and the length of pendulum is 16 m.

Frequency of an oscillation is the number of wave cycles per unit time. It is the inverse of time period. As the length of the pendulum increases, the frequency of oscillation decreases. Therefore, the shorter pendulum will have greater frequency.

Given time period of pendulum = 8 s.

then length of pendulum L = T²/4π² g.

l = 8²/4×π² × 9.8 m/s² = 16 m.

Frequency of the oscillation is the inverse of its time period. Hence, the frequency of the pendulum for a time period of 8 Hz is :

1/8 = 0.13 Hz.

Therefore, option a is correct.

Find more on frequency:

https://brainly.com/question/14926605

#SPJ1