3 positive test charge lie on the x axis,q1=25microcoloum,is at the origin ,q2=10microcoloumb is at x=2m and q3=20microcloumb is at x=3m.find the resultant force on q3?​

Answers

Answer 1

Answer:

the link is right here

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Related Questions

QUICK ITS DUE IN 6 MINUTES. create a scenario that applies the 3 laws of motion. Explain in complete sentences how each law if demonstrated

Answers

Answer:

In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

What are the different types of Boolean operations related to 3D modeling?

Answers

There are three main types of Boolean operations that are commonly used in 3D modeling:


1. Union: This operation combines two or more objects into a single object by merging their overlapping areas. This is useful for creating complex shapes by combining simpler ones.



2. Difference: This operation subtracts one object from another, creating a cavity or hole in the remaining object. This is useful for creating cutouts or removing unwanted sections of an object.


3. Intersection: This operation creates a new object that only includes the overlapping areas of two or more objects. This is useful for creating precise cuts or intersections between objects.


These Boolean operations are often used in combination with each other to create complex 3D models. They are supported by most 3D modeling software and are essential tools for creating detailed and intricate designs.

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Which two changes would decrease the electric force between two charged
particles?
A. Increase the distance between the particles.
B. Decrease the distance between the particles.
C. Increase the charge of both particles.
D. Increase the charge of one of the particles.
E. Decrease the charge of one of the particles.

Answers

Answer:

Decrease the charge of one of the particles

what must happen in order for a metaphoric rock to be transformed into a igneous rock

Answers

Answer:

If the newly formed metamorphic rock continues to heat, it can eventually melt and become molten (magma). When the molten rock cools it forms an igneous rock.

Explanation:

How are coal types classified?
color and texture
carbon content and heat value
depth from the surface
sulfur content

Answers

It’s carbon and it’s heat value

Answer:

I believe its B...."Carbon Content and Heat Value"

Explanation:

Coal is classified into four main types, or ranks: anthracite, bituminous, subbituminous, and lignite. The ranking depends on the types and amounts of carbon the coal contains and on the amount of heat energy the coal can produce.

describe how asteroids meteors and cometsmove around the solar system

Answers

Answer:

Explanation:

While traveling through space, asteroids sometimes collide with each other and break up into smaller fragments. Comets shed dust as they roam the solar system. These 'break ups' result in numerous small particles and fragments, called meteoroids, which orbit the sun. ... Thus a meteor, or shooting star, is formed.

Answer:

While traveling through space, asteroids sometimes collide with each other and break up into smaller fragments. Comets shed dust as they roam the solar system. These 'break ups' result in numerous small particles and fragments, called meteoroids, which orbit the sun. Thus a meteor, or shooting star, is formed.

Explanation:

Suppose a 100-gram mass, when attached to a spring, causes the spring to stretch 8 cm.
What would you expect a 25-gram mass to do when attached to the same spring?
(1 point)
O Stretch the spring 4 cm.
O Stretch the spring 8 cm.
O Stretch the spring 32 cm.
O Stretch the spring 2 cm.

Answers

Answer:Apparently the further displacement should be of other 3 cm; but, let's consider the development of the spring on one vertical plain, and fixed on a wall by the upper end.

Now the spring doesn't look circular; but as a stick fixed on the wall. Before placing the first 100 grams weight, the stick is not horizontal; but its overhanging end is lower by the measured length of the spring at rest. The length line of the spring with its horizontal projection line forms an angle.

The first 100 grams load is decomposed in function of the new angle: one component in line with the stick, the other one perpendicularly respect to it. The same happens with 200 grams.

The flection momentum is given by the perpendicular component of the load with respect to the stick line in overload, and the measure of the stick itself. Such component is inversely proportional to the other component, and decreases in relation to higher load while the other component (that doesn't produce flexion) encreases.

I assume that I can't calculate the new displacement because is not given the height of the spring at rest, the length of the development of the spring. Accordingly, I cannot calculate all various angles of the stick in relation with gravity.

Explanation:

When a 25 g mass is attached to the same spring, the spring is stretched by 2 cm.

What is Hook's law?

Hooke's law states that the applied force [F] equals a constant k times the displacement or change in length [x].

Mathematically - F = - Kx

Given is a situation in which a stretch of 8 cm is caused by a 100g mass.

From this, we can write -

Mass [m] = 100 g = 0.1 Kg

Displacement [x] = 8 cm = 0.08 m

According to the question -

The spring constant [K] can be calculated using Hook's law as -

F = -Kx

mg = -Kx

K = - mg/x

K = - (0.1 x 9.8) / 0.08

K = - 12.25 N/m

|K| = 12.25 N/m

Now, when mass [M] = 25g = 0.025 Kg, using Hook's law -

|F| = |- kx| = kx

Mg = 12.25x

x = Mg/12.25

x = (0.025 x 9.8)/12.25

x = 0.02

x = 2 cm

Therefore, when a 25 g mass is attached to the same spring, the spring is stretched by 2 cm.

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A snake is speeding up from rest to 8 mph to chase a meal. What is the change in velocity?

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The change in velocity of the snake is 8 mph.

The initial velocity of the snake is zero mph because it is starting from rest. The final velocity of the snake is 8 mph because that is its speed while chasing its meal.

Therefore, the change in velocity is:

final velocity - initial velocity = 8 mph - 0 mph = 8 mph

Velocity is a physical quantity that describes the rate at which an object changes its position with respect to time. It is a vector quantity, which means it has both magnitude and direction. The magnitude of velocity is the speed of an object, while the direction is the path it follows. Velocity is often expressed in meters per second (m/s) or kilometers per hour (km/h).

When an object moves, its velocity changes as it covers a certain distance in a certain amount of time. The formula for calculating velocity is velocity = distance/time. Therefore, if an object travels 10 meters in 2 seconds, its velocity is 5 m/s. Velocity can also be represented graphically on a distance-time graph, where the gradient of the line represents the velocity.

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Three identical train cars, coupled together are rolling east at 2.0 m/s. A fourth car traveling east at 4.0 m/s catches up with the three and couples to make a fourcar train. A moment later the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five car train. What is the speed of the five car train? Answer in m/s.

Answers

The train moves with common Velocity, then the velocity of 5 Car train is 2m/s

There are in total 5 identical train cars which collide with each other after some interval of time

Let the Train Cars be: A,B,C,D and E

So, Velocity of A,B and C = 2 m/s

Velocity of D = 4 m/s

Velocity of E = 0 m/s

Let's Assume that the mass of all the carts is 'x', as all are identical Coaches

The common Velocity of the 5 Car train (A+B+C+D+E) if they collide with each. other we have to find

We will use the law of conservation of momentum, which states that the initial momenta of objects = Final momenta of objects

m1u1 + m2u2 = m1V1 + m2v2

Given, Mass of Train Cars = x (Assumed)

Velocity of A,B,C = 2m/s

So, they are travelling on the track, so if they collide with D, their Initial momenta will be the same as final momenta.

As Given, their final velocity are equal. So,

a(ip) + b(ip) + C(ip) + d(ip) = a(vp) + b(vp) + C(vj)

Where, IP = Initial momentum

VP = final momentum

(2*x) + (2*x) + (2*x) + (4*x)

2x + 2x + 2x + 4x = v (x+x+x+x)

10x = 4xv

v = 10x/4x =

v = 2.5mps

Hence, The final velocity of (A,B,C,D) or Four Car train = 2.5 m/s

Now, After sometime travelling with same velocity, they collide with a stationary train car of same mass and it also start moving with same velocity.

aip + bip + Cip + dip + eip = avp + bvp

(10x) + (0*x) = (v*x) + (v*x) + (v*x) + (v*x)

(10x) + 0 = v(x+x+x+x+x)

10x = 5xv

v = 10x/5x

v = 2 mps

Hence, The speed of 5 Car train (A+B+C+D+E) = 2m/s

If the train moves with common Velocity, then the velocity of 5 Car train is 2m/s

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Choose a sport you like, such as football or gymnastics. Describe how a high level of flexibility would affect your performance in that sport. Consider the benefits in many aspects of the sport.

Answers

The level of flexibility will affect my performances in football. Football

requires some level of flexibility to do certain things.

Flexibility will enable me change speed and direction easily when there is a

counter attack by the opponents. It will also assist in using some techniques

such as adding more curve on the football with the feet in order to score

goals.

Flexibility will also ensure that there will be lesser injury concerns because there will be less sprains or other muscle related injuries.

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1) Calculate tension force in the string if the system accelerates up an inclined plane at 4m/s²

2) Calculate the magnitude of F if the system moves up the inclined plane at a constant velocity​

1) Calculate tension force in the string if the system accelerates up an inclined plane at 4m/s2) Calculate

Answers

1) As long as there is tension in the string connecting the two objects, they will both accelerate together with the same acceleration, 4 m/s². By Newton's second law,

• the net force on the 3-kg object acting parallel to the incline is

∑ F = F - T - f₃ - 3g sin(30°) = (3 kg) (4 m/s²)

• the net force on the 3-kg object perpendicular to the incline is

∑ F = n₃ - 3g cos(30°) = 0

• the net parallel force on the 6-kg object is

∑ F = T - f₆ - 6g sin(30°) = (6 kg) (4 m/s²)

• and the net perpendicular force on the 6-kg object is

∑ F = n₆ - 6g cos(30°) = 0

From the last two equations, it follows that

n₆ = 6g cos(30°) ≈ 50.9223 N

f₆ = 0.2 n₆ ≈ 10.1845 N

T - f₆ - 6g sin(30°) = 24 N   ⇒   T ≈ 63.5845 N ≈ 64 N

2) If the objects are pulled up the incline with constant velocity, then the acceleration of either object is zero. The free body diagrams stay the same, so we have the same equations using Newton's second law, the only difference is that each right side is zero.

The new tension in the string is then

T - f₆ - 6g sin(30°) = 0   ⇒   T ≈ 39.5845 N

From the second equation above, we find

n₃ = 3g cos(30°) ≈ 25.4611 N

f₃ = 0.1 n₃ ≈ 2.5461 N

Then in the first equation,

F - T - f₃ - 3g sin(30°) = 0   ⇒   F ≈ 56.8306 N ≈ 57 N

1) Calculate tension force in the string if the system accelerates up an inclined plane at 4m/s2) Calculate

What happens when a sound wave passes by the particles of a medium?

Answers

Answer:

Propagation of Sound Waves:

Sound waves move (propagate) through a medium by means of particle-to-particle interaction. The source disturbs the immediately surrounding particles, causing them to vibrate about their fixed position at the same frequency as the source.

Capacitance is the measure of a capacitors ability to store an electrical charge.
a. true
b. false

Answers

True

Capacitance is the ability of a component or circuit to collect and store energy in the form of an electrical charge.

what is electric charge?

Electric Charge is the property of subatomic particles that causes them to experience a force when put in an electric and magnetic field.  Electric charges are of two sorts: Positive and Negative, commonly carried by charge carriers protons and electrons.

Electric charge is a scalar quantity. Apart from having a magnitude and direction, a quantity to be named a vector ought to too comply the laws of vector addition, such as triangle law of vector addition and parallelogram law of vector addition; as it were at that point the amount is said to be a vector quantity. When two currents meet at a intersection, within the case of an electric current, the resultant current of these will be an algebraic sum and not the vector whole. Subsequently, an electric current may be a scalar quantity, in spite of the fact that it has magnitude and direction.

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Which is easier for a beginner? (This is for archery)

O long bow

O recurve bow

Answers

Answer:

The recurve bows

Explanation:Vote brainliest plz

The recurve bow is smaller and easier to handle while the longbow is used more for competitions. So I would say the recurve bow is easier for a beginner

The mass of the train is 450000 kg.
Calculate the maximum possible speed of the train at the end of the first 4.0km of the
journey.

Answers

The maximum possible speed of the train at the end of the first 4.0 km of the journey is 0 m/s.

To calculate the maximum possible speed of the train at the end of the first 4.0 km of the journey, we can apply the principle of conservation of energy.

Assuming there are no external forces like friction or air resistance, the initial potential energy of the train will be converted into kinetic energy.

The potential energy (PE) of the train at the beginning of the journey can be calculated as PE = mgh, where m is the mass of the train, g is the acceleration due to gravity (approximately \(9.8 m/s^2\)), and h is the height difference (in this case, we assume it to be zero).

The kinetic energy (KE) of the train at the end of the 4.0 km journey can be calculated as \(KE = (1/2)mv^2\), where v is the velocity of the train.

Since the potential energy is converted into kinetic energy, we can equate the two expressions:

PE = KE

\(mgh = (1/2)mv^2\)

Simplifying and canceling out the mass:

\(gh = (1/2)v^2\)

Substituting the values, \(g = 9.8 m/s^2\)and h = 0, we get:

\((9.8 m/s^2)(0) = (1/2)v^2\)

Simplifying further:

\(0 = (1/2)v^2\)

This equation tells us that the maximum possible speed of the train at the end of the first 4.0 km of the journey is 0 m/s.

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What is the position and kind of image produced by the lens below?

Complete the ray diagram to support your answer.​

What is the position and kind of image produced by the lens below?Complete the ray diagram to support

Answers

The answer is convex image

A gas at 300 kPa, is in a sealed container of volume 100 cm3 at 30°C. If the container is heated to 100°C, what is pressure of the gas inside the container?

Answers

Given:

Pressure, P = 300 kPa

Volume, V = 100 cm³

Temperature, T = 30°C

Let's fin the pressure of the gas inside the container if it is heated to 100°C.

Apply the Gay-Lussac's law:

\(\frac{P_1}{T_1}=\frac{P_2}{T_2}\)

Where:

P1 = 300 kPa

T1 = 30 + 273 = 303 K

T2 = 100 + 273 = 373 K

V1 = V2 (since the container is sealed).

Let's solve for P2.

Rewrite the formula for P2:

\(\begin{gathered} P_2=\frac{P_1T_2}{T_1} \\ \\ P_2=\frac{300*373}{303} \\ \\ P_2=\frac{111900}{303} \\ \\ P_2=369.31\text{ kPa} \end{gathered}\)

Therefore, the pressure if the container is heated to 100°C is 369.31 kPa.

ANSWER:

369.31 kPa

What happened to North American coastal waters when the great white shark population decreased?


The oyster population increased.


O The clam population increased.


The ray population increased.


The scallop population increased.

Answers

Answer:

The Ray Population Increases

Explanation:

This happens because the great white eats bigger animals

a soccer ball is kicked from level ground with an initial speed of 18 m/s at an upward angle of 44 degrees (relative to horizontal). a player 54 m away in the direction of the kick starts running to meet the ball at that instant. what must the player's average speed be in order to meet the ball just before it hits the ground?

Answers

The player must run at an average speed of 15.58 m/s towards the ball to meet it before it hits the ground.

A soccer ball is kicked from level ground with an initial speed of 18 m/s at an upward angle of 44 degrees (relative to horizontal). A player 54 m away in the direction of the kick starts running to meet the ball at that instant.

The time the ball takes to hit the ground can be calculated from its vertical motion alone.

From the initial velocity, we can deduce that

u= 18 m/sθ = 44°a= -9.8 m/s²

The time taken for the ball to fall can be calculated using the formula:

t = u sin θ /g  which implies, t = 18 sin44°/9.8 = 1.8 s.

If the player is to meet the ball before it hits the ground, then he must reach the point where the ball hits the ground exactly the same moment the ball hits the ground. If we assume the player reaches the point, x, where the ball hits the ground after time t,

then

54 + Vx t = x (1)

where Vx is the horizontal velocity of the player.

Now, the distance travelled by the ball in the horizontal direction in time t is given by

u cos θ t=18 cos44° *1.8 = 23.95 m.

Substituting the value of t in Eq. (1) gives:

54 + Vx (1.8) = 23.95Vx = (23.95-54)/1.8 = -15.58 m/s

As the player's speed should be positive, the absolute value of -15.58 m/s gives 15.58 m/s.

Hence the player must run at an average speed of 15.58 m/s towards the ball to meet it before it hits the ground.

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Which are benefits of using nuclear power plants to generate electricity?

Answers

Nuclear power plants have several benefits when it comes to generating electricity. One of the major advantages is that they produce a large amount of electricity. Nuclear reactors can generate more than 1,000 megawatts of electricity, making them highly efficient.

Additionally, nuclear power plants do not emit greenhouse gases, which helps reduce the impact of climate change. Another benefit is that nuclear power plants have a continuous power output, as they do not rely on weather conditions like solar or wind power. Furthermore, nuclear power plants require less fuel compared to traditional power plants, reducing the cost and dependency on fossil fuels. Lastly, nuclear power plants can operate for long periods of time without interruption, providing a reliable source of electricity. Overall, nuclear power plants offer a reliable, efficient, and low-carbon alternative for generating electricity.

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3. Sandy pushes a 1000 kg car with a force of 800 N. Charlie helps her push the car in the same direction with a force of 700 N. What is the rate of acceleration for the car ?

Answers

Answer:

a = 1.5 m/s^2

Explanation:

Total force = 700 + 800 = 1500 N

then because   F = ma

                         1500 N  = 1000 kg  *  a

                                a = 1.5 m/s^2

Review Question: (i) A loop lying in the same plane as a wire is moved from below toward the current-carrying wire with current pointing in the left direction. As the loop is moving, is there a (a) clockwise current around the loop, a (b) counterclockwise current, or (c) no current? (ii) What if the loop moves from above? (iii) What if the loop moves parallel to the wire to the left below it?

Answers

(i) As the loop is moved from below toward the current-carrying wire with the current pointing in the left direction, there will be a counterclockwise current around the loop. This is due to the interaction between the changing magnetic field produced by the current in the wire and the loop. According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electric current in a nearby conductor.

(ii) If the loop moves from above toward the current-carrying wire, the direction of the induced current will be clockwise. The change in the relative motion between the loop and the wire alters the orientation of the induced current, following the principles of electromagnetic induction.

(iii) When the loop moves parallel to the wire to the left below it, there will be no current induced in the loop. The motion of the loop in a parallel direction to the wire does not result in a changing magnetic field, which is necessary to induce an electric current according to Faraday's law. Therefore, no current will be generated in this scenario.

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what is atmospheric pressure​

Answers

Answer:

the pressure within the atmosphere of Earth

Explanation:

Atmospheric pressure is a force in an area pushed against a surface by the weight of the atmosphere of the earth.

determine the magnitude of the force between two parallel wires 24 m long and 3.0 cm apart, each carrying 75 a in the same direction.

Answers

The magnitude of the force between two parallel wires is 3.60 N.

To determine the force between two parallel wires, we use Ampere's Law. The formula for calculating the force per unit length (F/L) between two parallel wires is:

F/L = μ₀ * I₁ * I₂ / (2 * π * d)

Where:
- F/L is the force per unit length
- μ₀ is the permeability of free space (4π × 10⁻⁷ Tm/A)
- I₁ and I₂ are the currents in the wires (75 A each)
- d is the distance between the wires (3.0 cm = 0.03 m)

F/L = (4π × 10⁻⁷ Tm/A) * 75 A * 75 A / (2 * π * 0.03 m) = 120 N/m

Now, multiply the force per unit length by the length of the wires (24 m) to find the total force:

F = (120 N/m) * 24 m = 3.60 N

So, the magnitude of the force between the two parallel wires is 3.60 N.

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Derive velocity-time relation from velocity-time graph ​

Answers

Explanation:

hope this helps you

.....,.......

Derive velocity-time relation from velocity-time graph

A girl kicks a blue ball with a velocity of 20.0 m/s at 65.0o. How long is it in the air?


1.85s

1.92s

13.6s

3.69s

Answers

Explanation:

t = usin©/g

Where t is the time to reach the maximum height

Time spent in air is T = 2t

Hence, T = 2usin©/g

T = 2 x 20 x sin 65°/ 9.8

T = 3.69s

now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. it fires a ball straight out of the cannon as it moves. after it is fired, what happens to the ball?

Answers

The cart fires a ball straight out of the cannon as it moves. after it is fired, the ball falls behind the cart.

A theoretical or conceptual model known as projectile motion is the combination of a uniform horizontal motion (with constant velocity) and a vertical launch (governed by the acceleration of gravity).

When the ball is thrown vertically upward, it falls behind the cart. Assume that the cart is moving at a velocity of v\(_{x}\) at the time. While the cart accelerates horizontally, the ball follows the typical parabolic trajectory of a projectile.

The projectile's constant horizontal component, v\(_{x}\), is the ball's velocity. The ball completes its parabolic motion after t, and because the cart is subject to acceleration, its final velocity is greater than the projectile's horizontal velocity. As a result, the projectile is pushed behind the cart.

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A truck pulls a trailer on a flat stretch of road. The forces acting on the trailer are
the force due to gravity (250 000 N downward), the force exerted by the road
(250 000 N upward), and the force exerted by the cable connecting the wailer to
the truck (20 000 N to the right). The forces acting on the truck are the force due to
gravity (80 000 N downward), the force exerted by the road (80 000 N upward), the
force exerted by the cable (20 000 N to the left), and the force causing the truck to
move forward (26 400 N to the right).

Answers

The net vertical force on the trailer is 0, while the net horizontal force on the trailer is 20,000 N to the right.

The net vertical force on the truck is 0, while the net horizontal force on the truck is 6,400 N to the right.

The given parameters;

the trailer:

force on the trailer due to gravity, Fg = 250,000normal force on the trailer due to the road, N = 250,000 Nhorizontal force on the trailer, Fx = 20,000 N to the right

the truck:

force on the truck due to gravity, Fg = 80,000 Nnormal force on the truck due to the road, N = 80,000 Nleft horizontal force on the truck, Fx = 20,000 Nright horizontal force on the truck, Fx = 26,400 N

The net force on each vehicle is calculated as follows;

for the trailer:

Net vertical force is calculated as;

\(\Sigma F_y = 250, 000 \ N - 250,000 \ N = 0\)

Net horizontal force is calculated as;

\(\Sigma F_x = 20,000 \ N\)

for the truck;

Net vertical force is calculated as;

\(\Sigma F_y =80,000 \ N - \ 80,000 \ N = 0\)

Net horizontal force is calculated as;

\(\Sigma F_x = 26,400 \ N - \ 20,000 \ N = 6,400 \ N \ to \ the \ right\)

"Your question is not complete, it seems to be missing the following information;"

find the net force on each vehicle.

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A bullet of mass 50 g is fired from below into a suspended object of mass 450 g. The object rises through a height of 1.8 m with bullet remaining inside the object. Find the speed of the bullet. Take g = 10 ms².​

Answers

Hello!

We can begin by using the Work-Energy theorem. The initial energy is the kinetic energy of the combined mass of the bullet and suspended object, while the final energy is the GPE of the combined objects.

In equations:
\(E_i = \frac{1}{2}mv^2\\\\E_f = mgh\)

m = combined mass of the bullet and suspended object (0.5 kg)
v = velocity of block system after struck (? m/s)
g = acceleration due to gravity (10 m/s²)

h = final height of combined objects (1.8 m)


Set the two equal (Conservation of Energy) and solve for velocity.\(\frac{1}{2}mv^2 = mgh \\\\\frac{1}{2}v^2 = gh \\\\v^2 = 2gh \\\\v = \sqrt{2gh}\\\\v = \sqrt{2(10)(1.8)} = 6 \frac{m}{s}\)

Now, we can use the conservation of linear momentum to solve.

Recall that:
\(p_i = p_f\)

For an inelastic collision (objects stick together):

\(m_1v_1 + m_2v_2 = (m_1 + m_2) v_f\)

Let m1 represent the bullet and m2 represent the suspended object.

Initially, the suspended object has no velocity, so v2 = 0. Therefore:

\(m_1v_1 = (m_1 + m_2)v_f\\\\v_1 = \frac{(m_1 +m_2)v_f}{m_1}\\\\v_1 = \frac{(0.5)(6)}{0.05} = \boxed{60 \frac{m}{s}}\)

How much aetarny is required to acceferate a spaceship With a rest mass of 110 metric tont to a tobed of 0.456 e? Tries 0/12 Every day our Earth receives 1.550×10 23
, eneroy from the Sun. If we were able to use 1.05 percent of this energy to accestrate spacaulias, then hew many missions would be possibie in one year? Tries 0/12

Answers

Given, Mass of spaceship = 110 metric tonne Rest mass = m0 = 110 tonne = 110000 kg Velocity of spaceship = 0.456e = 0.456 × 3 × 108 m/s = 1.368 × 108 m/s We know that the formula for calculating the total energy required to accelerate an object is given by; E = γm0c²[(v/c)² - 1].

Where, E is the total energy required to accelerate an object.γ is the Lorentz factor.m0 is the rest mass of the object. V is the velocity of the object. c is the speed of light in vacuum. Substituting the given values in the above formula; E = γm0c²[(v/c)² - 1]γ = 1 / √[1 - (v/c)²] = 1 / √[1 - (1.368 × 108/3 × 108)²]γ = 2.08E = 2.08 × 110000 × (3 × 10⁸)² [((1.368 × 10⁸) / (3 × 10⁸))² - 1]E = 2.08 × 110000 × (9 × 10¹⁶) [(0.456)² - 1]E = - 2.08 × 110000 × (9 × 10¹⁶) × 0.742E = - 1.3092 × 10²⁵ J. The total energy required to accelerate a spaceship with a rest mass of 110 metric tonne to a speed of 0.456c is 1.3092 × 10²⁵ J.

Neglecting the energy required for atmospheric drag and gravitational losses, and assuming that the entire 1.550 × 10²³ J of energy received from the sun per day can be used to accelerate a spaceship, the number of missions possible in a year can be calculated as follows. Number of missions per day = (1.05/100) × 1.550 × 10²³ J Number of missions per year = (1.05/100) × 1.550 × 10²³ J × 365 days Number of missions per year = 5.722 × 10²³ J × 365 days Number of missions per year = 2.090 × 10²⁷ J. Thus, the number of missions that can be possible in a year will be 2.090 × 10²⁷ J.

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