Determine the voltage dropped across

a) The kinetic energy of the dart after it is thrown is 2.376 J.

b) The speed of the dart is 18.45 m/s.

c) If the dart were thrown straight upwards, the maximum height it would reach is 17.0 m.

a) The work done on the dart by the applied force is given by:

work = force x distance = 4.40 N x 0.54 m = 2.376 J

Since no energy is lost due to friction, all of this work is converted to the kinetic energy of the dart:

kinetic energy = work = 2.376 J

b) The kinetic energy of the dart can also be expressed as:

kinetic energy = (1/2) x mass x velocity^2

Rearranging this equation gives:

velocity^2 = (2 x kinetic energy) / mass

Substituting the values from part a) gives:

velocity^2 = (2 x 2.376 J) / 0.028 kg = 340.29 m^2/s^2

Taking the square root of both sides gives:

velocity = 18.45 m/s

c) When the dart is thrown straight upwards, its initial vertical velocity is zero. The maximum height it will reach can be calculated using the formula:

maximum height = (initial velocity^2) / (2 x acceleration)

where acceleration is the acceleration due to gravity, which is approximately 9.81 m/s^2.

Substituting the speed calculated in part b) gives:

maximum height = (18.45 m/s)^2 / (2 x 9.81 m/s^2) = 17.0 m

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Answer:

(C) it is moving to the right wrt to the ground

The crate is accelerated to the right (wrt the ground) because the frictional force between the truck bed and the crate is to the right and it is this force that provides movement to the crate

Answer : a) The crate will be moving in the negative x direction (to the left) when it falls off the truck. The force of the acceleration of the truck in the positive x direction will push the crate in the negative x direction. This will cause the crate to move away from the truck in the negative x direction. Correct answer is option B

This is because the truck is accelerating in the positive x direction (to the right), and the crate, being free to move, will have the same acceleration as the truck. This will cause the crate to slide backwards off the truck in the negative x direction.

Therefore, the crate will be moving in the negative x direction (to the left) when it falls off the truck.

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A hair dryer uses the electricity from the power source to run its motor and heating element when it is hooked into an electrical outlet. Heat and kinetic energy are created from this electrical energy.

One of the most frequent causes of circuit breakers being tripped by a hairdryer is an overloaded circuit. A circuit overload occurs when there are several high-powered gadgets drawing 15 to 20 amps of electricity simultaneously on the same circuit.

A conventional in-room, wall-mounted hair dryer uses roughly 1.6 kW of power on average. This indicates that a guest will use 0.4 kilowatt-hours (kWh) of power if they use their hair dryer for 15 minutes.

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Your friend is correct. In order to determine the speed at which the person who leaves point B must walk, you need to know the length of AC and BC.

This is because the time it takes for each person to reach point C is dependent on the distance they must travel and the speed at which they are traveling.

Using the formula time = distance / speed, you can calculate the time it takes for each person to reach point C.

For the person leaving point A, the time it takes to reach point C is tA = AC / 3, since they are traveling at a speed of 3 miles per hour.

For the person leaving point B, the time it takes to reach point C is tB = BC / x, where x is the speed at which they are traveling.

Since both people are intended to reach point C at the same time, you can set the two equations equal to each other:

AC / 3 = BC / x

Cross-multiplying and solving for x gives you the speed at which the person leaving point B must walk:

x = 3BC / AC

Without knowing the length of AC and BC, you cannot determine the speed at which the person leaving point B must walk. Therefore, your friend is correct.

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Answer:

The specific heat capacity of water is 4.184 J/g°C, and we need to find the amount of heat required to raise the temperature of 10 kg (or 10,000 g) of water from 20°C to 100°C.

The formula for calculating the amount of heat required is:

Q = m * c * ΔT

where:

Q = heat energy (in Joules)

m = mass (in grams)

c = specific heat capacity (in J/g°C)

ΔT = change in temperature (in °C)

We can start by calculating the change in temperature:

ΔT = 100°C - 20°C = 80°C

Then, we can plug in the values and solve for Q:

Q = 10,000 g * 4.184 J/g°C * 80°C

Q = 3,347,200 J

Therefore, Peter needs 3,347,200 Joules of heat to raise the temperature of his 10 kg vat of water from 20°C to 100°C.

The distance covered by the body after 15 seconds down the inclined plane is approximately 1102.5 meters.

We can use the equations of motion to solve this problem. The acceleration of the body down the inclined plane can be found using trigonometry:

a = gsin(30°) = (9.8 m/s²)(1/2) = 4.9 m/s²

where g is the acceleration due to gravity.

Using the equation of motion:

s = ut + (1/2)at²

where s is the distance covered, u is the initial velocity (which is zero in this case), and t is the time taken, we can find the distance covered after 15 seconds:

s = (1/2)4.9(15)² = 1102.5 meters

Therefore, the distance covered by the body after 15 seconds down the inclined plane is approximately 1102.5 meters.

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Digital data can be encoded by a computer program and are easy to change by a computer program. Therefore, options A and D are correct.

A and D are two reasons why digital storage of data is more secure than analogue storage.

A - Digital data can be encoded using various encryption techniques that make it more difficult for unauthorized individuals to access or interpret the data.

D - Digital data are easy to change or modify using a computer program, but this can also be a security advantage as it allows for quick updates and corrections to be made, and changes can be tracked and logged for security purposes.

B and C are not necessarily unique to digital storage, and may also be applicable to analogue storage. Fingerprint or facial ID can be used to protect physical storage devices, and a strong password can also be used to secure both digital and analogue storage.

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Answer:

A. Digital data can be encoded by a computer program.

B. Digital data can be protected by a fingerprint or facial ID.

Explanation:

did quiz

The correct answer is option: e. Because, this force always acts along  line joining the two charges. For like charges, the force is repulsive in nature.

The Coulomb's law states how charges interact with each other. That law states that: [tex]F =q1q24πϵ0r2[/tex]

If the charges are like , the force will be repulsive, meaning that each charge will exert a force on the other to push the two of them apart. If  charges are opposite , they will exert an attractive force on each other. G or unlike charges, the force is attractive as shown below: ( as Shown in image attached  to question), As we know none of the arrow moves in the direction of the net force. Hence, the correct answer is option: e

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The amount of information available, the length of time available to examine it, and consequently the complexity of weather occurrences limit one's ability to express their skill to predict the weather.

Models employ estimations and assumptions to forecast the weather because it is impossible to collect data from the future. These estimations from the models get less accurate as time goes on since the atmosphere is continually changing.

Probabilistic techniques accurately depict the uncertainty where deterministic plans provide exact average quantities with a known but unquantified uncertainty.

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If the pressure in the pipe is 8940 n/m and in the constricted section is 6705 n/m ,the rate at which oil is flowing is approximately 0.029 m^3/s.

We can use the principle of continuity of flow to relate the flow rate of the oil in the pipe to the difference in pressure and the area of the pipe at the constriction:

Q = Av

where Q is the flow rate, A is the area of the pipe at the constriction, and v is the velocity of the oil at the constriction.

We can use Bernoulli's equation to relate the pressure difference to the velocity of the oil at the constriction:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

where P1 and P2 are the pressures at the two points, and v1 and v2 are the velocities of the oil at those points.

Since the pipe is horizontal, the height difference between the two points can be neglected and we can assume that the gravitational potential energy of the oil is constant. Therefore, we can simplify Bernoulli's equation to:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

Solving for v2, we get:

v2 = sqrt((P1 - P2) / (1/2ρ) + v1^2)

Now we can substitute this expression for v2 into the continuity equation:

Q = Av1 = A sqrt((P1 - P2) / (1/2ρ) + v1^2)

Solving for Q, we get:

Q = A v1 sqrt(2(P1 - P2)/ρ(A^2 - a^2))

where A is the area of the larger section of the pipe and a is the area of the constriction.

Substituting the given values, we get:

Q = (pi/4)(0.567 m)^2 (v1) sqrt(2((8940 N/m^2) - (6705 N/m^2))/(821 kg/m^3)((0.567 m)^2 - (0.045 m)^2))

Q ≈ 0.029 m^3/s

Therefore, the rate at which oil is flowing is approximately 0.029 m^3/s.

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A modern large wind turbine can generate about 250 kw of electricity, whereas a large nuclear power plant can generate 1,000 mw so, 4000 wind turbines would be required to give the same output as one nuclear power plant.

To know how many wind turbines would be required to give the same output as one nuclear power plant is a simple mathematical calculation that involves only the conversion of kilowatts to megawatts.

Wind turbine and Nuclear power plant electricity generation in modern large wind turbine with moderate winds is 250 KW whereas, the generation capacity of large nuclear power plant is 1,000 MW.

To determine how many wind turbines would be required to give the same output as one nuclear power plant, we need to convert kilowatts to megawatts.

Since 1 MW = 1,000 kW, therefore 1,000 MW = 1,000,000 kW

We are given that a modern large wind turbine can generate about 250 kW of electricity

Therefore, the number of wind turbines required to give the same output as one nuclear power plant can be calculated as:

Number of wind turbines = Total capacity of nuclear power plant / Capacity of single wind turbine

                                         = 1,000,000 / 250= 4000

Thus, 4,000 wind turbines would be required to give the same output as one nuclear power plant.

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Answer:

0.1 KM/S

Explanation:

First, looking at the question we can say a few things: distance = speed/time. First we will change the 72 KM/HR to ? KM/S (seconds). To change the units fo the speed to seconds, we need to find how many seconds are in an hour which is 3600) then we have 72 KM/3600S and we will divide 3600 by 5 to get 720 which is what we will divide 3600 by to get to 5 seconds and what we will divide 72 by to get your speed in kilometers for your answer. 3600/720 = 5 seconds, and 72/720 is equal to 0.1. To format your answer, you would get 0.1 KM/S (kilometers/seconds)

If your teacher won't accept that answer or you want to change the unit of measurement for speed, you can also find out how many feet/miles a kilometer is and then multiply 0.1 times that value and then you'd have ? ft/s or mi/s.

This implies that when the force applied on an item increases, so does the object's acceleration. Similar to how an object's acceleration decreases as its mass increases, so does its mass.

Force with acceleration are directly correlated, as shown by Newton's second law. The more force that is exerted to an object, the faster it will accelerate. For instance, the acceleration doubles when the force exerted on an object doubles.

The relationship among acceleration and force is explained in Newton's second laws of motion. They are comparable in size. An object moves forward at a speed equal to the force pushing against it. The simplest approach to determine force is to multiply mass by acceleration.

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The polarizing axis of the second pane of the window make with the polarizing axis of the first pane of the window in order to reduce the intensity of the sunlight to 34% of the original value is [tex]23^o[/tex].

The intensity of the sunlight falling from the first pane

[tex]I_1 = \frac{I_o}{2}[/tex]

Once this intensity light passes through the second pane then

[tex]I_2 = I_1 \cos^2 \thetaI_2 = \frac{I_o}{2} \cos^2 \theta[/tex]

Given I2 /Io = 0.42  (42%) so

[tex]0.42 = \frac{1}{2} \cos^2 \theta\\[/tex]

[tex]\cos^2 \theta = 0.84[/tex]

[tex]\cos \theta = \sqrt{0.84} = 0.9165\\[/tex]

[tex]\theta = \cos^{-1} ( 0.9165) = 23.6^o[/tex]

The polarizing axis, also known as the polarization direction, is the direction of the electric field oscillation of an electromagnetic wave. When light passes through a polarizing filter, only the component of the electric field parallel to the polarizing axis is allowed to pass through, while the perpendicular component is blocked.

For example, a linear polarizing filter has a polarizing axis that allows only light waves oscillating in a specific direction to pass through. If the electric field oscillation of the light is perpendicular to the polarizing axis, it will be blocked, resulting in a darker image. In contrast, circular polarizers have a rotating polarizing axis that can selectively block light waves based on their direction of rotation. This is useful in photography and other applications where glare or reflections need to be minimized.

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Answer:

10.17 m/s in the direction the compact car was going (+)

Explanation:

Law of conservation of momentum states that total P before the collision must equal total momentum after the collision.

P = mv

solve for v, velocity of the two cars stuck together after the collision:

(187kg)(-38 m/s) + (702kg)(23 m/s) = (187 + 702 kg)v

         momentum before               =   momentum after

-7106 kg·m/s + 16146 kg·m/s = 889 kg(v)

9040 kg·m/s = 889 kg(v)

v = 9040 kg·m/s / 889 kg = 10.17 m/s

Answer:

the bottom

Explanation:

The number of electrons in 1 nenocoulomb (1 nc) charge is 6.24*109. It takes 6 10 18 electrons to produce one coulomb of charge.

The smallest elemental component of an atom, the electron has a negative charge. In some kind of a negative ion, there are an adequate amounts of electrons as well as protons. One electron but one proton are all that the hydrogen atom has.

The negatively charged components of an atom are called electrons. The total negative charge of an atom's electrons counteracts the positive electrical charge of its protons there in atomic nucleus. When compared to all the other components of the atom, electrons are quite tiny.

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The power consumed by the resistor when it is connected to a 12.5 V battery is 4.41 W and the voltage of the battery is 13.41 V which provides 5 W power to the resistor.

We can use the formula for the power consumption of a resistor:

[tex]P = V^2/R[/tex]

where P is power, V is voltage, and R is resistance.

a. To determine the power consumption of the resistor when attached to a 12.6 V battery, we can use the same formula and solve for P:

[tex]P = V^2/R = (12.6 V)^2 / R[/tex]

However, R is not given in the problem. But we can use the power and voltage values given when the resistor was connected to a 1.5 V battery to find R:

[tex]P = V^2/R[/tex]

[tex]0.0625 W = (1.5 V)^2 / R[/tex]

[tex]R = (1.5 V)^2 / 0.0625\ W[/tex]

[tex]R = 36 \ \Omega[/tex]

Now we can use this value of R to find the power consumption when the resistor is connected to a 12.6 V battery:

[tex]P = V^2/R = (12.6 V)^2 / 36 \ ohms[/tex]

P = 4.41 W

Therefore, the power consumption of the resistor when attached to a 12.6 V battery is approximately 4.41 W.

b. To find the voltage of the battery that consumes 5.00 W, we can use the same formula and solve for V:

[tex]P = (V^2) / R[/tex]

[tex]5.00 W = (V^2) / R[/tex]

We know the value of R from before, so we can substitute it in:

[tex]5.00 W = (V^2) / 36 \ ohms[/tex]

Solving for V, we get:

[tex]V = \sqrt{5.00 W \times 36 \ ohms} = 13.41 V[/tex]

Therefore, the voltage of the battery that consumes 5.00 W is approximately 13.41 V.

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Overall, the difference between detached and semi-detached binary systems lies in the extent to which the stars interact with each other and exchange mass.

In a detached binary system, the two stars are far enough apart from each other that they do not significantly interact with each other. The stars have their own gravitational fields, which cause them to orbit around the common center of mass, but they do not exchange significant amounts of mass or significantly alter each other's evolution. Detached binary systems are the most common type of binary systems.

In contrast, in a semi-detached binary system, one of the stars is closer to the common center of mass than the other and is therefore more strongly affected by the gravitational pull of the other star. The closer star can transfer mass to the more distant star, often through an accretion disk, causing the more distant star to become more massive and the closer star to become less massive over time. Semi-detached binary systems can lead to various phenomena such as accretion disks, mass transfer, and outbursts of energy.

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If you were in a rocket ship traveling away from earth at a speed close to the speed of light, then the changes that you would notice in the clock and the volume of your friend who stayed on earth are time dilation and volume dilation.

Time dilation: According to special relativity theory, time dilation occurs as an object's velocity approaches the speed of light. The faster an object travels, the slower its internal clock ticks. Time would seem to pass more slowly for you than it would for your friend on earth. The time on the rocket would appear to be slower than the time on the earth, and the rocket's clock would tick more slowly as seen from the earth.

Volume dilation: Volume dilation is a term used to describe a length contraction or expansion of an object along the direction of motion. According to the Lorentz transformation, as the velocity of an object approaches the speed of light, its length appears to shrink in the direction of motion.

This would result in the volume of the object appearing to decrease in size as well. Your friend on earth would notice that your rocket ship appears to be shorter than it really is, and its volume would appear to be less.

Therefore, time dilation and volume dilation are the two factors that would be noticed.

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the block when it is being hauled up the slope at a constant speed using force F perpendicular to a ramp, with a force of 10.0N.

Force is indeed a physical phenomenon that alters or has the potential to alter an object's shape, its state of motion, or both.

According to Newton's second law of motion, the force corresponds to the momentum change divided by the time change. Force equals mass times acceleration, or F = m x a, for a constant mass.

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The height of a water-filled manometer required to measure blood pressure as high as 300 mm Hg is 229.69 cm.

A manometer is a pressure measurement device that is utilized to measure the pressure of gases and liquids in a container.

The weight of the liquid in the manometer rises or falls depending on the pressure of the gases and liquids in the container.

In order to measure blood pressure, a water-filled manometer is used. The density of blood is 1.05 x 103 kg/m3. The height of the manometer is required to be found.

The pressure of blood is 300 mm Hg.

The following formula will be used to calculate the height of the manometer:

h = (P*d)/(g*H2O)

where, P = 300 mm Hg,

d = 1.05 × 103 kg/m^3,

g = 9.8 m/s2, and

H2O = 1000 kg/m^3

Substituting the values in the equation:

h = (300*1.05*103)/(9.8*1000)

h = 229.69 cm

The height of the manometer must be 229.69 cm to measure blood pressure as high as 300 mm Hg.

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The X component of the tiger's velocity is 53.59 km/h.

The vertical (Y) component of the tiger's velocity is 12.37 km/h.

The components of the tiger's velocity include X and Y components; the magnitudes of the X and Y components is calculated using the following formula.

The X component of the tiger's velocity is calculated as;

Vx = V cosθ

where;

Vx = 55 km/h  x  cos (13)

Vx = 53.59 km/h

The vertical (Y) component of the tiger's velocity is calculated as;

Vy = V sinθ

Vy = 55 km/h  x sin (13)

Vy = 12.37 km/h

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A pail of water is swung in a vertical circle using a uniform circular motion. In order to make sure that the water doesn't spill out when the pail is upside down, a minimum constant tangential speed of 2.1 m/s is required.

The minimum constant tangential speed required by the pail of water in order to ensure that the water doesn't spill out when the pail is upside down can be calculated using the formula:

[tex]v = \sqrt{gr}[/tex]

where v = minimum constant tangential speed g = acceleration due to gravity r = radius of the circle.

The distance from the bottom of the pail to Sarah's shoulder is 0.449 m long.

Since this distance is the radius of the circular path, we can substitute it in the formula.

Therefore,

[tex]v = \sqrt{9.8 m/s^2 \times 0.449 \ m} = \sqrt{4.4102 m^2/s^2} = 2.1 \ m/s[/tex]

Therefore, the minimum constant tangential speed required by the pail of water is approximately 2.1 m/s.

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Therefore, the coefficient of kinetic friction is approximately 0.136

the acceleration of the first crate with friction down the ramp.

We'll use the following formula:

a = gsin(theta) - mucos(theta)*g

whereg = acceleration due to gravity = 9.8 m/[tex]s^2[/tex]

theta = angle of the ramp = 25 degrees

mu = coefficient of kinetic friction

Plugging in the values, we get:

a = 9.8sin(25) - mucos(25)9.8

a = 3.9763 - 3.5299mu

Plugging in the values, we get:

[tex]v^2=[/tex] 0 + 2*(3.9763 - 3.5299*mu)6

[tex]v^2[/tex] = 47.715 - 42.1794mu

the velocity of the second crate without friction at the bottom of the ramp. We know it's 2.5 times the velocity of the first crate with friction, so:v' = 2.5sqrt(47.715 - 42.1794mu)

no friction for the second crate, we can use the conservation of energy to relate the initial potential energy to the final kinetic energy:

mg6sin(25) = 0.5m*[tex]v^2[/tex]

where

g = acceleration due to gravity = 9.8 m/

Simplifying and plugging in the value for v', we get:

mg6sin(25) = 0.5m*)(47.715 - 42.1794mu)

3.5299 = 11.885 - 10.545*mu

mu = 0.136

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(a) The tension in the hitch is 339.75 N.

equal to the mass of the trailer times the acceleration (453 kg x 0.75 m/s2 = 339.75 N).
(b) The force of static friction exerted by the road on the pickup truck is  1038.75 N.
(c) The force the trailer exerts on the pickup truck is equal to 339.75 N.

(a) The tension in the hitch is equal to the mass of the trailer times the acceleration.

It is calculated by,

453 kg x 0.75 m/s2

= 339.75 N.

(b) The force of static friction exerted by the road on the pickup truck to propel it forward is equal to the mass of the pickup truck times the acceleration

It is calculated by

1385 kg x 0.75 m/s2

= 1038.75 N

(c) The force the trailer exerts on the pickup truck is equal to the mass of the trailer times the acceleration.

It is calculated by,

453 kg x 0.75 m/s2

= 339.75 N

Static friction is a force that keeps an object at rest. Static friction definition can be written as: The friction experienced when individuals try to move a stationary object on a surface, without actually triggering any relative motion between the body and the surface on which it is on.

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The correct answer in that the Radio waves have a longer wavelength than microwaves.

Radio waves have a wavelength range of about 1 millimeter to 100 kilometers, while microwaves have a wavelength range of about 1 millimeter to 1 meter. This means that radio waves have a longer wavelength than microwaves in general. Wavelength is related to the frequency of the electromagnetic wave by the equation: λ = c / f, where λ is the wavelength, c is the speed of light, and f is the frequency. Since the speed of light is constant, a longer wavelength corresponds to a lower frequency and vice versa. Radio waves are commonly used for communication and broadcasting, while microwaves are used for a variety of applications including cooking food, radar, and wireless communication. Understanding the properties of different electromagnetic waves, including their wavelength and frequency, is important for many areas of science and technology.

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According to the question, The pressure that the weight lifter's feet now exert on the floor is approximately 431200 Pa.

The amount of matter in an entity or particle is represented by the dimensionless number mass (symbolized m). The kilogram is the International System's (SI) preferred measure of mass. (kg).

The weight lifter's weight calculated as:

Weight = mass x gravity

Weight lifter's weight = 140 kg x 9.8 m/s^2 = 1372 N

The weight of the mass the weight lifter picks up is:

Weight of the mass = mass x gravity = 300 kg x 9.8 m/s^2 = 2940 N

Therefore, the total weight exerted by the weight lifter and the mass is:

Total weight = Weight lifter's weight + Weight of the mass = 1372 N + 2940 N = 4312 N

The pressure exert on the floor can be calculated as:

Pressure = Force / Area

Assuming the weight lifter's weight is distributed equally on both feet and each foot has an area of approximately 50 cm^2,

the pressure on each foot calculated as:

Pressure on each foot = Total weight / (2 x Area of each foot)

Pressure on each foot = 4312 N / (2 x 50 cm^2 x 0.0001 m^2/cm^2) = 4312 N / 0.01 m^2 = 431200 Pa

Therefore, the pressure that the weight lifter's feet now exert on the floor is approximately 431200 Pa.

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Answer:

B

Explanation:

The moon effects the Earth's tides more than the sun.

The correct statement for the formation of tides on Earth is "The Moon has the greatest effect on tides since it is closer to Earth than the Sun."

Tides are caused by the gravitational pull of the Moon and Sun on Earth's oceans.

While the Sun has a greater mass than the Moon, the Moon is much closer to Earth and therefore has a greater effect on the tides.

The Moon's gravitational pull causes the oceans to bulge towards it, creating high tides on the side of Earth closest to the Moon and on the opposite side of Earth.

As Earth rotates, different areas experience high and low tides. The Sun also has an effect on the tides, but it is less significant than the Moon's effect.

In conclusion, the statement "The Moon has the greatest effect on tides since it is closer to Earth than the Sun" is true for the formation of tides on Earth.

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Answer:

Let the mass of the ball be m, and let v be the velocity of the ball before it is caught. Let the final velocity of the person and ball be 0 after the catch. We can write the following equation:

(m)(v) + (78 kg)(3 m/s) = (m + 78 kg)(0 m/s)

Simplifying this equation, we get:

(m)(v) = -234 kg m/s

We also know that the initial velocity of the ball is 34 m/s, so we can write another equation using this information:

(m)(34 m/s) = (m)(v)

Substituting the first equation into the second equation, we get:

(m)(34 m/s) = -234 kg m/s

Solving for m, we get:

m = -234 kg m/s / (34 m/s) = -6.88235 kg

This is a negative mass, which doesn't make sense. We made an error in our calculations, possibly due to significant figures. Let's try again with more precision:

(m)(34.0 m/s) = -234 kg m/s

m = -234 kg m/s / 34.0 m/s = 6.88235 kg

Rounding to the appropriate number of significant figures, we get:

m ≈ 6.9 kg

Therefore, the ball would need to have a mass of approximately 6.9 kg in order to stop a 78 kg person moving at 3 m/s when they catch it.

Explanation: