the pilot of an airplane notes that the compass indicates a heading due west. the airplane's speed relative to the air is 100 km/h. the air is moving in a wind at 31.0 km/h toward the north. find the velocity of the airplane relative to the ground.

Answer:

By the law of conservation of momentum, the total momentum of the system before and after the push must be equal. Therefore, we can use the following equation to solve for Jill's velocity:

(mass of Jack) x (velocity of Jack) = (mass of Jill) x (velocity of Jill)

Plugging in the given values, we get:

(64.3 kg) x (2.19 m/s) = (45.4 kg) x (velocity of Jill)

Solving for the velocity of Jill, we get:

velocity of Jill = (64.3 kg x 2.19 m/s) / 45.4 kg = 3.10 m/s (eastward)

Therefore, Jill's body is propelled eastward with a velocity of 3.10 m/s.

Malus's law describes how much light is transmitted when a beam of polarised light travels through a polarizer:

I = I0 cos^2(θ)

where is the angle formed by the transmission axis of the polarizer and the polarisation direction of the input light, and I0 is the beam's starting intensity.

The transmission axis of the polarizer in this issue makes a 35.0 degree angle with the vertical. The angle between the transmission axis and the polarisation direction is 90 - 35.0 = 55.0 degrees since the incident light is horizontally polarised.

By applying the provided values to Malus's law, we obtain:

I0 cos2 = 0.55 W/m2 (55.0 degrees)

To solve for I0, we obtain:

I0 equals 0.55 W/m2/cos2 (55.0 degrees)

I0 = 1.24 W/m^2 (rounded to two major values) (rounded to two significant figures)

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Answer:

Explanation:

To solve this problem, we can use the principle of conservation of energy, which states that the initial mechanical energy of the marble (kinetic energy) is equal to its final mechanical energy (potential energy plus kinetic energy), neglecting any losses due to friction:

Initial kinetic energy = Final potential energy + final kinetic energy

1/2 mv^2 = mgh + 1/2 mv_f^2

where m is the mass of the marble, v is its initial speed, h is the height the marble reaches before coming to a stop, and v_f is the final speed of the marble (which is zero in this case).

(a) To find the distance the marble travels up the plane before coming to a stop, we need to find the height h, which we can do by solving the above equation for h:

h = (1/2 v^2)/(g sinθ)

where g is the acceleration due to gravity (9.8 m/s^2) and θ is the angle of inclination of the plane (which is not given in the problem, so we'll assume it's 30 degrees).

Plugging in the given values, we get:

h = (1/2 × 7.0^2)/(9.8 × sin30) = 6.4 m

Therefore, the marble travels 6.4 meters up the plane before coming to a stop.

(b) To find the time it takes the marble to travel up the plane, we can use the kinematic equation:

v_f = v_i + at

where v_i is the initial velocity (7.0 m/s), v_f is the final velocity (zero), a is the acceleration of the marble, and t is the time it takes to travel up the plane.

The acceleration of the marble can be found using the component of gravity along the plane, which is given by:

a = g sinθ

Plugging in the values, we get:

0 = 7.0 + (9.8 sin30)t

Solving for t, we get:

t = (7.0/4.9) sec = 1.4 sec

Therefore, the marble takes 1.4 seconds to travel up the plane.

Answer:

the resistance of the copper wire 20 meters long and with a diameter of 0.05 cm is 0.342 ohms.

Explanation:

To calculate the resistance of the copper wire, we need to use the formula:

R = (ρ * L) / A

where R is the resistance of the wire, ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire.

The resistivity of copper is 1.68 × 10^-8 Ω·m.

First, we need to calculate the cross-sectional area of the wire:

A = π * (d/2)^2

A = π * (0.05cm/2)^2

A = 0.0019635 cm^2

Note that we converted the diameter from centimeters to meters, since the resistivity is given in ohms per meter.

Now, we can calculate the resistance of the wire:

R = (ρ * L) / A

R = (1.68 × 10^-8 Ω·m * 20m) / 0.0019635 cm^2

R = 0.342 Ω

Therefore, the resistance of the copper wire 20 meters long and with a diameter of 0.05 cm is 0.342 ohms.

The power input to the heat pump is 25 kW.

The COP (coefficient of performance) of the heat pump is 4.0. This means that for every unit of power consumed by the heat pump, it supplies four units of heat to the building.

The rate at which the heat pump supplies heat to the building is 100 kW.

Therefore, the power input to the heat pump can be calculated as:

Power input = Power output / COP

Power input = 100 kW / 4.0

Power input = 25 kW

Hence, the power input to the heat pump is 25 kW.

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if the particle velocity is perpendicular to the magnetic field lines, the force experienced by the particle will be the largest.

The force experienced by a moving charged particle in a magnetic field is given by the formula:

F = q v B sin(theta)

where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and theta is the angle between the velocity of the particle and the magnetic field.

The force experienced by the particle is maximum when sin(theta) is equal to 1, i.e., when the angle theta between the velocity of the particle and the magnetic field is 90 degrees. This means that the velocity vector of the particle is perpendicular to the magnetic field lines.

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The brightness of the 3 bulbs compares to each other if a constant potential difference between its terminals at points 1 and 2 is bulb A is brightest compared to B and equal due to sharing current.

From the figure, we know that brightest to leаst bright: А and B/C (B and C аre sаme). B аnd C аre in the sаme brаnch, so they both hаve the sаme current. Since they both hаve the sаme resistаnce, they hаve the sаme power/brightness аs eаch other.

Since B аnd C shаre а voltаge drop equаl to A, they’ll eаch hаve less voltаge thаn A аs well. With less current АND less voltаge thаn A, they’ll both be dimmer thаn A. BC hаs аn equivаlent resistаnce of 1/2 А. This meаns the voltаge drop аcross BC is 1/2 the voltаge аcross А.

Your question is incomplete, but most probably your full question can be seen in the Attachment.

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Electrons from the student's hair to the plastic comb. When the student runs the comb through her hair, the comb and the hair rub against each other. This friction causes the transfer of electrons between the two materials.

Friction is a force that opposes motion between two surfaces in contact. Whenever two surfaces are in contact and one of them moves or tries to move over the other, there is a force that resists the motion. This force is called friction. Friction arises due to the irregularities on the surfaces of the objects in contact. When the two surfaces are pressed together and moved relative to each other, the irregularities interlock and create resistance to motion. The force of friction always acts in the opposite direction to the direction of motion or the direction of the applied force.

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The most fundamental stage of studying matter and energy is quantum physics. It aims to comprehend the traits and behaviours of the very substances that make up nature.

According to this theory, the universe of any object transforms into an array of parallel universes with an identical number of possible states for that object, one in each universe. This occurs as soon as the potential for any object to be in any state arises.

By examining the interactions between particles of matter, quantum physicists investigate how the universe functions. This career might suit your interests if you like math or physics.

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Yes, adding too many fins on a surface can cause the overall heat transfer coefficient and heat transfer to increase.

This is because the presence of fins can increase the surface area available for heat exchange, allowing more heat to be transferred over a given period of time. Fins can also improve the convective heat transfer coefficient and turbulence levels of the surrounding fluid.
When adding fins to a surface, it is important to consider the fin spacing and height to ensure that the fins do not impede the flow of the surrounding fluid. For instance, if the fins are too close together, they can cause an increase in the pressure drop of the fluid and reduce the efficiency of the heat exchange. Likewise, if the fins are too high, they can block the flow of the fluid.
It is also important to consider the type of material used for the fins. Fin materials can affect the thermal conductivity of the fins, which in turn can influence the heat transfer rate. Furthermore, if the fins are made from a material that is not resistant to corrosion, the effectiveness of the fins may be reduced over time.
In summary, adding too many fins on a surface can cause the overall heat transfer coefficient and heat transfer to increase. It is important to consider the fin spacing, height, and material when determining the most efficient fin configuration for a given surface.

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Answer:

To solve this problem, we can use the law of conservation of momentum, which states that the total momentum of a system is conserved in the absence of external forces. In this case, the system consists of the hockey puck and the goalie.

Before the catch, the momentum of the puck is:

puck momentum = m1 * v1 = 0.2 kg * 24 m/s = 4.8 kg m/s

where m1 is the mass of the puck and v1 is its velocity.

The momentum of the goalie before the catch is zero since the goalie is at rest.

After the catch, the combined momentum of the puck and the goalie is:

combined momentum = m1 * v2 + m2 * v3

where v2 is the velocity of the puck after the catch, v3 is the velocity of the goalie and m2 is the mass of the goalie with the equipment.

Since the system is closed and there are no external forces, the momentum is conserved. Therefore:

puck momentum = combined momentum

4.8 kg m/s = 0.2 kg * v2 + 75 kg * v3

Solving for v3, the velocity of the goalie after the catch, we get:

v3 = (4.8 kg m/s - 0.2 kg * v2) / 75 kg

We need to find v2, the velocity of the puck after the catch. Since the puck is caught and held, its velocity is zero.

Substituting v2 = 0 into the above equation, we get:

v3 = 4.8 kg m/s / 75 kg = 0.064 m/s

Therefore, the goalie (with the puck) slides on the ice with a speed of 0.064 m/s.

The work done by the weight lifter is 7260 J.

The weight lifter does 7,260 J of work when lifting the 390-N weights. This is calculated by multiplying the force (390 N) by the distance (1.80 m) that the weights were moved.

W = Fd, where W is work, F is force, and d is distance.

The weight lifter must apply a force to lift the weights. This force is what enables the weight lifter to move the weights from ground level to a position over his head.

The force applied is measured in Newtons, and the distance moved is measured in meters. The work done is measured in joules (J).

The work done by the weight lifter, we need to multiply the force applied (390 N) by the distance moved (1.80 m). So, W = Fd, W = 390 N x 1.80 m, and W = 7,260 J.

This is the work done by the weight lifter in lifting the 390-N weights from ground level to a position over his head.

It is important to note that the work done is the same whether the weight lifter moves the weights at a constant speed or at varying speeds.

The only factor that affects the amount of work done is the amount of force applied and the distance the weights were moved.

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The distance between the two bicycles at t=0 is 15.6 meters.

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line. To find the distance between the two bicycles at time t=0, we need to find their positions at that time.

For the first bicycle,

X1 = -6.0 m + (7.5 m/s)t

    = -6.0 + 7.5 × 0

    = -6.0 m.

For the second bicycle,

X2 = 9.6 m + (-4.5 m/s)t

     = 9.6 + (-4.5) × 0

     = 9.6 m.

Therefore, the distance between the two bicycles at time t=0 is:

Distance = X2 - X1

               = 9.6 m - (-6.0 m)

               = 15.6 m

So the distance between the two bicycles at t=0 is 15.6 meters.

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The magnitude of force required to stop a 4000-kg car initially traveling at 10 m/s in 20.0 s is 2,00 N.

The magnitude of force is mass into acceleration.

But we know that acceleration is velocity into time.

Therefore force =(mass*velocity)/time

In this problem, the car has a mass of 4,000 kg and is initially traveling at a velocity of 10 m/s.

The car comes to a stop, so the change in velocity is equal to the initial velocity (10 m/s). The time taken to stop the car is 20.0 seconds.

Substituting these values into the formula, we get:

force = (4,000 kg *10 m/s) / 20.0 s

Simplifying this expression, we get:

force = 200 N

Therefore, the magnitude of force required to stop a 4,000-kg car initially traveling at 10 m/s in 20.0 s is 200 N.

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The mass of the spaceship when it is traveling at half the speed of light would be approximately 6.91 x 10¹¹ kg.

The spaceship's mass at half the speed of light can be calculated using the formula:

m = m₀ / √(1 - v²/c²)

where m = mass at speed v, m₀ = rest mass, v = velocity, and c = speed of light.

The rests mass of the spaceship is 660,000 tons, which we can convert to kilograms by multiplying by 907,185 (1 ton = 907,185 kg).

So, m₀ = 660,000 * 907,185

= 5.98 x 10¹¹ kg.

The spaceship is traveling at half the speed of light, which we can express as v = 0.5c, where c = 299,792,458 m/s. Plugging these values into the equation, we get:

m = m₀ / √(1 - v²/c²)

m = (5.98 x 10¹¹ kg) / √(1 - (0.5c)²/c²)

m = (5.98 x 10¹¹ kg) / √(1 - 0.25)

m = (5.98 x 10¹¹ kg) / √(0.75)

m = (5.98 x 10¹¹ kg) / 0.866

m = 6.91 x 10¹¹ kg

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Each plate has a charge that is roughly 113.17 pC in size.

According to the equation Q=CV, where Q is the charge in Coulombs, C is the capacitance in Farads, and V is the potential difference between the plates in volts, Both the capacitance and the applied voltage affect how much charge moves into the plates.

We can use the following formula to determine the size of the charge present on each plate of a parallel-plate capacitor:

Q = CV

It is critical to remember that the parallel-plate capacitor's capacitance is determined by:

C = εA/d

It makes use of the free space permittivity (0).

We'll assume that the provided capacitance of 7.9 pF is accurate.

Using the formula Q = CV, we get:

Q = (7.9 pF) x (14.3 V) = 113.17 pC

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When Einstein's theory of gravity (general relativity) gained acceptance, it demonstrated that Newton's theory had been (b) incomplete.

Newton's theory of gravity is a law that governs the behavior of objects. The formula [tex]F = \frac {G m_1  m_2}{ d^2}[/tex] explains the force of gravity between two objects, where F is the force of gravity, G is the universal gravitational constant, m1 is the mass of one object, m2 is the mass of another object, and d is the distance between the centers of the two objects. This formula shows that gravity decreases as distance increases.

Einstein's theory of gravity (general relativity): It is a theoretical framework proposed by Albert Einstein in 1915. It combines special relativity and Newton's law of universal gravitation. General relativity is based on the notion that gravitation is not a force acting between two masses but rather a curvature of spacetime created by the presence of massive objects. It differs from Newton's law of universal gravitation, which states that gravitation is caused by an attractive force acting between two masses.

When Einstein's theory of gravity (general relativity) gained acceptance, it demonstrated that Newton's theory had been incomplete. Therefore the correct answer is b.

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In a model ensemble system, meteorologists change the initial conditions each time they run a simulation of the same model.

An ensemble forecasting system consists of a group of forecasts for the same event that are produced using different input conditions. The model ensembles are created by initiating the forecasting system many times, each time with a different input or initial condition set, and then averaging the results to reduce the effect of errors due to the choice of the initial condition.

The forecast can be viewed as a probability distribution for the event, rather than a single forecast.The model ensemble forecasting technique can also improve confidence in forecasting by reducing the uncertainty caused by the different input conditions that can cause a significant error in the final results. The technique is most effective when the models being used are at least slightly different, but not so different as to be incompatible with one another.

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The time it takes for the ball to reach the ground is 1.63 seconds.
The magnitude of the final velocity of the ball is 17.2 m/s.

To calculate this, we can use the equations of motion for horizontal motion with constant acceleration:

x = x0 + v0t + (1/2)at2

v2 = v02 + 2a(x - x0)

Here, x

is the initial velocity (17.2 m/s), x is the final distance (11.0 m), and a is the acceleration due to gravity (-9.8 m/s).
Substituting in the given values, we get:

11.0 m = 2.0 m + (17.2 m/s)(t) + (-9.8 m/s2)(t2)/2

(17.2 m/s)2 = (17.2 m/s)2 + 2(-9.8 m/s2)(11.0 m - 2.0 m)
Since the initial velocity was directed horizontally, the magnitude of the final velocity is the same as the initial velocity (17.2 m/s).

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The satellite's centripetal acceleration is 0.0131 m/s2.

The centripetal acceleration is a = (7.8 km/s)2/(7.0 x 106 m) = 0.0131 m/s2.

The centripetal acceleration of a satellite in a low Earth orbit with a radius of 7.0 x 10^6 m and a speed of 7.8 km/s can be calculated using the equation a = v2/r, where a is the centripetal acceleration, v is the speed, and r is the radius.

Centripetal acceleration is the acceleration that points towards the center of a circular path and is responsible for keeping an object moving in a circular path.

From the formula, it is evident that centripetal acceleration is directly proportional to the square of the velocity of the object and inversely proportional to the radius of the circular path.

This means that higher speeds or smaller circular paths require larger centripetal accelerations to keep the object moving in a circle.

Centripetal acceleration can be provided by various forces, depending on the situation.

For example, when a car rounds a curve, the friction between the tires and the road provides the centripetal acceleration. In the case of an object in orbit around a planet, such as a satellite, the gravitational force of the planet acts as the centripetal force that keeps the object in a circular path.

Centripetal acceleration is a fundamental concept in physics and has numerous practical applications in various fields, including transportation, sports, and astronomy.

Understanding centripetal acceleration is crucial for comprehending the dynamics of circular motion and designing systems that involve objects moving in circular paths, such as vehicles on curved roads or satellites in orbit.

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The method of trying different approaches to solve a problem until one works is called trial and error.

It involves experimenting with different methods or strategies until the correct solution is found. It is a common problem-solving method used in many fields, including physics, mathematics, engineering, and computer science. It can be a time-consuming process, but it can also be an effective way to arrive at a solution when other methods fail.

What is trial and error method?

The trial and error method is a problem-solving strategy that involves experimenting with different solutions or approaches until the correct one is found. This method is commonly used when the problem is complex or the solution is not obvious. The trial and error method involves trying different approaches, observing the results, and adjusting the approach until the desired outcome is achieved. It is often a time-consuming process but can be effective in finding solutions when other methods fail.

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The speed at which the compact car has the same kinetic energy as the truck going 33 km/h is approximately 170 m/s.

The formula for calculating kinetic energy is K.E. = 1/2 x mass x speed². Therefore, the speed of the compact car is the

[tex]\sqrt{(32266/982)} * 33[/tex]  km/h = 126.46 km/h.

The kinetic energy (KE) of an object is given by the formula:

[tex]KE = 1/2 * m * v^2[/tex]

where m is the mass of the object and

v is its velocity.

We are given the masses and velocities of the compact car and the truck. Let's calculate the kinetic energy of the truck first:

[tex]KE_{(truck)}= 1/2 * m_{truck} * v_{truck}^2[/tex]

[tex]KE_{(truck)}= 1/2 * 32266* (33)^2[/tex] (kg )*(km/h)²

[tex]KE_{(truck)} = 1.42*10^9[/tex] J

Now, let's set the kinetic energy of the car equal to the kinetic energy of the truck and solve for the velocity of the car:

[tex]KE_{(car)} = KE_{truck}[/tex]

[tex]1/2 * m_{(car)} * v_{(car)}^2 = 1.42*10^9[/tex] J

Rearranging the equation, we get:

[tex]v_{(car)}^2 = (2 * KE_{truck}) / m_{(car)}[/tex]

[tex]v_{car}^2 = (2 * 1.42*10^9)/982[/tex]J/kg

[tex]v_{car}^2= 2.89*10^6[/tex] m²/s²

Taking the square root of both sides, we get:

[tex]v_{car} = \sqrt{2.89*10^2}[/tex] m²/s²

[tex]v_{car}[/tex]=170 m/s

Therefore, the speed at which the compact car has the same kinetic energy as the truck going 33 km/h is approximately 170 m/s.

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The peak voltage across a 500-w device connected to a 120-v ac power source is 120 V. This is because the voltage rating of the device is determined by the voltage of the power source.

To calculate the peak voltage across the device, we can use Ohm's Law:

V = I x R.

This equation states that the voltage is equal to the current multiplied by the resistance.

We know that the voltage of the power source is 120 V and the current is 4 A (I = P/V, where P is the power rating of the device). Therefore, the resistance is 30 ohms (R = V/I).

We can then use Ohm's Law to calculate the peak voltage across the device.

V = I x R
V = 4 A x 30 ohms
V = 120 V

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Answer:  The charge on the capacitor increases exponentially as the capacitor charges. As time goes on, the rate of charging decreases, and the charge on the capacitor approaches Qmax. The charge on the capacitor does not change once it is fully charged.

An uncharged capacitor is connected in series with a battery and a resistor. When the circuit is closed, the current begins to flow, and the capacitor begins to charge. The voltage across the capacitor increases as the capacitor charges.

When a battery, resistor, and uncharged capacitor are connected in series, the charge of the capacitor changes as a function of time according to the equation:

Q = Qmax(1 - e^(-t/RC))

An uncharged capacitor is connected in series with a battery and a resistor. When the circuit is closed, the current begins to flow, and the capacitor begins to charge. The voltage across the capacitor increases as the capacitor charges.

When the voltage across the capacitor is equal to the battery voltage, the current stops flowing through the circuit. The capacitor is then fully charged, and the charge on the capacitor is Qmax. At this point, the voltage across the capacitor is equal to the battery voltage, and the current through the resistor is zero.

The charge on the capacitor, Q, changes as a function of time, t, according to the equation:

Q = Qmax(1 - e^(-t/RC))

where Qmax is the maximum charge on the capacitor, R is the resistance of the resistor, C is the capacitance of the capacitor, and e is the base of natural logarithms.

The charge on the capacitor increases exponentially as the capacitor charges. As time goes on, the rate of charging decreases, and the charge on the capacitor approaches Qmax. The charge on the capacitor does not change once it is fully charged.



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Answer:

Γ = F X R

If the force is right angle to the lever arm then

Γ = F R = 42 N * .17 m = 7.1 N-m

The maximum speed at which the car can traverse the curve without slipping is 14.2 m/s.

The maximum speed that a car can traverse an unbanked curve without slipping is determined by the centripetal force acting on the car, which is provided by the force of static friction between the road and the car's tires.

The formula for centripetal force is given by:

F_c = m*v² / r

where Fc is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the curve.

The maximum speed of the car can be determined by equating the centripetal force to the maximum static friction force:

F_f = μs * m * g

where Ff is the maximum static friction force, μs is the coefficient of static friction, m is the mass of the car, and g is the acceleration due to gravity.

Setting these two equations equal to each other and solving for v, we get:

m*v²/ r = μ_s * m * g

v² = μ_s * g * r

v = [tex]\sqrt{Ms * g * r)}[/tex]

Plugging in the given values, we get:

v = [tex]\sqrt{0.67 * 9.81 m/s^{2} * 50 m)}[/tex]

v = 14.2 m/s

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The ratio of the current, Ib/Ia = 1/4.6

The ratio of the currents in wires A and B, Ib/Ia, is determined by the ratio of their resistances.

To understand this more clearly, consider the following equation:
V = I R

This equation states that the voltage across a wire is equal to the product of the current in the wire and its resistance. Since the same voltage is placed across both wires, and the resistance of wire B is greater than that of wire A, the current in wire B must be less than that of wire A. Therefore, the ratio of the currents is the inverse of the ratio of their resistances.

Solving we get,

(Ib/Ia) = (V/4.6R) / (V/R) = 1/4.6.

In summary, when the same voltage is placed across two wires with different resistances, the ratio of the currents in those two wires is equal to the inverse of the ratio of their resistances.

Therefore, if the same voltage is placed across wires A and B, the ratio of the currents, Ib/Ia will be equal to 1/4.6.

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The recoil speed of the archer is 2.07 m/s in the opposite direction of the arrow. This can be calculated using the conservation of momentum.

Momentum is defined as mass multiplied by velocity and is conserved during collisions.

The initial momentum of the archer-arrow system is 77.11 kg x 98.89 m/s = 7,624.14 kg m/s.

Since the arrow has a mass of 101 g, its velocity after the shot is 0 m/s, resulting in a final momentum of 7,523.14 kg m/s.

Since the total momentum is conserved, the velocity of the archer must be equal to the difference between the initial and final momentum divided by the mass of the archer: (7,624.14 - 7,523.14) / 77.11 = 2.07 m/s.

Therefore, the recoil speed of the archer is 2.07 m/s.

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The speed of the 2.86 g marble after the collision is 1.05 m/s.

We can use the conservation of momentum to solve this problem:

Before the collision:

m1 = 6.63 g = 0.00663 kg (mass of the first marble)

v1 = 1.41 m/s (velocity of the first marble)

m2 = 2.86 g = 0.00286 kg (mass of the second marble)

v2 = 0 m/s (initial velocity of the second marble)

After the collision:

v1' = 0.86 m/s (final velocity of the first marble)

v2' = ? (final velocity of the second marble)

Using conservation of momentum:

[tex]m1v1 + m2v2 = m1v1' + m2v2'[/tex]

Substituting the known values:

[tex]0.00663 kg * 1.41 m/s + 0.00286 kg * 0 m/s = 0.00663 kg * 0.86 m/s + 0.00286 kg * v2'[/tex]

Solving for v2':

[tex]v2' = (0.00663 kg * 1.41 m/s - 0.00663 kg * 0.86 m/s) / 0.00286 kgv2' = 1.05 m/s[/tex]

Therefore, the speed of the 2.86 g marble after the collision is 1.05 m/s.

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The acceleration of the trolley is acceleration = (220 g) / m.

What is acceleration defined as, the rate of change of velocity with respect to time. As acceleration has both a magnitude and a direction, it is a vector quantity. It is also the first derivative of velocity or the second derivative of position with respect to time.

Total force = 200 g + 20 g

= 220 g

where the acceleration brought on by gravity, or g, equals (9.8 m/s²).

We may now use Newton's second law of motion, which states that an object's net force is equal to its mass times its acceleration:

Net force = total force

= 220 g

Mass of the trolley is not given in the problem. Let's assume that it is m.

m * acceleration = 220 g

Solving for acceleration, we get:

acceleration = (220 g) / m

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Question:

A trolley is being pulled by a force that is equal to the weight of two masses, one with a weight of 200 g and the other with a weight of 20 g. Sketch a free-body diagram of the trolley and calculate its acceleration assuming there is no friction or resistance acting on it. (7)

Assume that the trolley is on a flat, level surface and is not initially moving. Additionally, assume that the weight units are in grams.