a bullet penetrates 7 cm into a piece of wood when fired at a speed of 33 m/s. find the time required for the bullet to stop.

In a circle at constant speed, the work done is zero since the Force is always perpendicular to the distance moved as you move incrementally around the circle.

An object moves in a circle at a consistent speed in a motion known as uniform circular motion. Any point on a propeller, for instance, that is rotating continuously, is moving uniformly in circles. The second, minute, and hour hands on a watch are some further examples. It is amazing that despite the constant rotation rate, points on these revolving objects are actually speeding. We must consider the motion in terms of vectors in order to see this.

A centripetal motion is an Objects having a constant speed have zero acceleration in one-dimensional kinematics. In two- and three-dimensional kinematics, a particle can experience acceleration even if its speed is constant if it follows a curved trajectory, like a circle.

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Yes, turning up the thermostat in the middle of the night for 15 minutes reduce the amount of time it takes it to reach temp in the morning.

The United States Department of Energy suggests turning thermostats back 7 to 10 degrees from their normal settings for 8 hours per day in order to achieve annual savings of up to 10%. The Department of Energy estimates that savings of approximately 1 percent can be achieved for each degree of thermostat adjustment that is made every 8 hours. The amount of time it takes for the temperature to reach the desired level in the morning can be reduced by raising the thermostat for fifteen minutes in the middle of the night.

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Answer:

To keep the other four charges in equilibrium, the charge q that should be placed at the center of the square is equal in magnitude but opposite in sign to the total charge of the other four charges.

Assuming that range aliasing can be tolerated and there are no other targets between the moon and Earth, a pulse repetition frequency of around 10-20 MHz would likely be sufficient for mapping the moon surface.

The maximum pulse repetition frequency (PRF) that can be used for mapping the surface of the moon is determined by the need to avoid range ambiguities and to achieve the desired resolution. The PRF is the number of pulses emitted per second. A high PRF allows for high resolution mapping but also increases the chance of range ambiguities.

If range ambiguities can be tolerated, a high PRF can be used to achieve a high resolution map. The altitude of the spacecraft, the size of the antenna, and the desired resolution of the map are also factors that determine the maximum PRF. A general estimate is that a PRF of around 10-20 MHz would be sufficient for mapping the surface of the moon with a high resolution.

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Answer:

Approximately [tex]3.59\times 10^{22}\; {\rm N}[/tex] (assuming that the orbit is circular.)

Explanation:

When an object is in a circular orbit of radius [tex]r[/tex] with a (linear) speed of [tex]v[/tex], the centripetal acceleration of this object would be [tex]a = (v^{2} / r)[/tex]. If the mass of the object is [tex]m[/tex], magnitude of the net force on this object would be [tex]F = m\, a = (m\, v^{2} / r)[/tex].

Look up the mass of the Earth: [tex]m \approx 5.9722\times 10^{24}\; {\rm kg}[/tex].

Look up the radius of the orbit (mean distance between the Earth and the Sun): [tex]r \approx 1.4960\times 10^{11}\; {\rm m}[/tex] (one Astronomical Unit.)

It is given that the linear orbital speed is [tex]v = 3.00 \times 10^{4}\; {\rm m\cdot s^{-1}}[/tex].

Therefore, magnitude of the centripetal force (net force) on the Earth would be:

[tex]\begin{aligned}F &= m\, a = \frac{m\, v^{2}}{r} \\ &\approx \frac{(5.9722 \times 10^{24}\; {\rm kg})\, (3.00 \times 10^{4}\; {\rm m\cdot s^{-1}})^{2}}{1.4960 \times 10^{11}\; {\rm m}} \\ &\approx 3.59 \times 10^{22}\; {\rm N} \end{aligned}[/tex].

The maximum speed the car weighing 1500kg and turning in a horizontal circle which has a radius of 20 meters can take the turn without skidding at 10.84m/s.

Maximum speed is the highest rate of speed that can be attained. Acceleration is the velocity, and because velocity has both a magnitude and direction associated with it, the acceleration changes when an object change the magnitude of their motion, the direction of their motion, or both of these.

Radius of the circular path, r = 20 m

Mass of the car, M = 1500 kg

Maximum speed of the car = v

The coefficient of friction, μ = 0.6

The centrifugal force will balance the friction force so that the car does not slip.

Therefore, mv²/r = μmg

v²/r = μg

v² = μgr

v = √(μgr)

v = √(0.6 × 9.8 × 20)

v = √(117.6)

v = √(294,000)​

v = √(117.6)

v = 10.84m/s

Therefore, the maximum velocity of the car is 10.84 meter per second.

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The SI unit of K so that the equation Velocity = K x density is correct is given as

K=m^4/s-kgK= m4/s−kg

Velocity is described as the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.

The SI unit of velocity is m/s and the Si unit of density is kg/m^3kg/m3 .

Adding the SI units of both quantities, we have that  :

m/s=K\times kg/m^3m/s=K×kg/m3

In terms of dimensions,

[LT^{-1}]=K\times [ML^{-3}][LT−1]=K×[ML−3]

Dimension of K is :

[K]=[M^{-1}L^4T^{-1}][K]=[M−1L4T−1]

SI unit of K is :

K=m^4/s-kgK=m4/s−kg

Hence,  the required solution is  K=m^4/s-kgK=m4/s−kg

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The change in the car's gravitational potential energy from A to B is calculated as 4.90 J.

Gravitational potential energy may be characterized as a type of energy that is typically possessed or acquired by an object due to an alteration in its position when it is present in a gravitational field. In more simple terms, it can be revealed that gravitational potential energy is an energy that is associated with gravitational force or gravity.

According to the question,

The formula for gravitational potential energy is as follows:

where m is the mass (in kg) of the body. G is the magnitude of the gravitational field that the body is exposed to. H is the height at which the body is located.

First, you have to calculate the gravitational potential energy of the car on point A, i.e. U₁= (2.0 kg)(9.8 m/s²)(0 m)= 0 J.

Second, the Gravitational potential energy of the car on point B is found as, U₂= (2.0 kg)(9.8 m/s²)(0.25 m)= 4.90 J.

Now, you must have to calculate the change in the car’s gravitational potential energy: ΔU= U₂-U₁= 4.90 J - 0 J= 4.90 J.

Therefore, the change in the car's gravitational potential energy from A to B is calculated as 4.90 J.

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The useful output power of the blender is 420 W.

To calculate the useful output power of the blender, we can use the equation:

P_output = P_input * efficiency

Where P_output is the useful output power, P_input is the total input power, and efficiency is the percentage of input power that is converted to useful output power.

Given that the total input power is 600 W and the blender is 70% efficient, we can substitute these values into the equation to find the useful output power:

P_output = 600 W * 0.70

P_output = 420 W

Therefore, the useful output power of the blender is 420 W.

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The speed of the penny after 2.5 seconds is 24.5 m/s.

What is speed?

Speed is a scalar quantity that refers to "how fast an object is moving." It is the rate at which an object changes its position, and it is measured in units of distance per unit of time (such as meters per second or miles per hour). Speed is related to the distance traveled by an object and the time it takes to travel that distance, and it can be calculated by dividing the distance traveled by the time it took to travel that distance.

The speed of an object in free fall can be calculated using the equation:

v = g * t

where v is the velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2 on the Earth's surface) and t is the time elapsed.

In this scenario, the penny is dropped off the top of the Statue of Liberty, which is 93 m tall, and we want to find the speed of the penny after 2.5 seconds.

So, we can substitute the values in the equation:

v = 9.8 m/s^2 * 2.5 s = 24.5 m/s

Therefore, the speed of the penny after 2.5 seconds is 24.5 m/s (assuming no air resistance).

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The statement that is false is "there are places on earth where all forces are absent." Forces, such as gravity, are always present on Earth.

All the given statements are true except the statement "there are places on earth where all forces are absent." is false.

Forces change the momentum of a body,forces always occur in equal and opposite pairs (Newton's third law), where there is no force, objects continue to move the way they were moving, and forces cause an acceleration to take place are all true statements about forces.

Newton's third law simply states that there is an equal and opposite reaction to every action. So, if object A exerts a force on object B, object B will exert an equal but opposite force on object A.

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Roughly 1,700 km/h. The Earth rotates faster than sound near the equator.

How quickly rotates the Earth close to the equator?

The Earth's circumference is around 40,075 kilometres at the equator; multiplying this by the length of the day yields a spin speed of approximately 1670 kilometres per hour.

How many times does the equator revolve in a day?

Each 24-hour day, the Earth rotates once around its axis. The speed of Earth's spin at its equator is around 1,000 miles per hour (1,600 km per hour). Every day of your existence, this day-night spin has taken you outside and under the sun and stars.

Can people feel the Earth's spin?

The speed of Earth is rapid. It orbits the Sun at a speed of roughly 67,000 miles (107,000 kilometres per hour), spinning (rotating) at about 1,000 miles (1600 kilometres) per hour. Due to the consistent speeds, we are not aware of any motion.

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Around 1,700 km/h.Correct!. Its circumference is approximately 40,075 kilometers at the equator; multiplying this by the length of the day yields a value of 1670 kilometers per hour for the equator-bound speed of rotation.

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If we neglect the effect of air friction, then the motion of the ball a short time later will be a combination of horizontal and vertical motion.

If you stand on tall cliff and throw ball so that it is initially moving purely horizontally and neglecting the effect of air friction, motion of the ball a short time later will be combination of horizontal and vertical motion. This is because the only force acting on ball is gravity, which will pull the ball downwards. Therefore, ball will experience a vertical acceleration due to gravity, while continuing to move horizontally at constant velocity.

Motion of the ball is a parabolic path, which is the trajectory of projectile under the influence of gravity. Horizontal component of the motion will remain constant, while vertical component will be affected by gravity and will decrease until ball reaches maximum height and then it will increase again until the ball hit the ground.

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The change in position or displacement (Δx) divided by the time intervals (Δt) in which the displacement occurs yields the average velocity.

Depending on the sign of the displacement, the average velocity can be positive or negative.

To begin, in order to calculate average velocities, we need the position for each instant mentioned:

Y(2) = 2 ft

Y(2.5) = 0 ft

Y(2.1) = 13.44 ft

Y(2.05) = 14.76 ft

Y(2.01) = 15.7584 ft

Let us now compute the average velocities:

V(2 - 2.5) = Y(2.5) - Y(2) / 2.5 - 2

= -32 ft/s

V(2 - 2.1) = Y(2.1) - Y(2) / 2.1 - 2

= -25.6 ft/s

V(2 - 2.05) = Y(2.05) - Y(2) / 2.05 - 2

= -24.8 ft/s

V(2 - 2.01) = Y(2.01) - Y(2) / 2.01 - 2

= -24.16 ft/s

Now, we can derive the expression for y for the instantaneous velocity:

For t=2s, V(t) = 40 - 32t V(2) = -24ft/s

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When the red barge collides with the blue barge, which has a mass of 1000000 kg, its final velocity with in collision elastic becomes 0.311 m/s.

The given data:

Using the law of conservation of momentum.

Following the formula, the red barge's final velocity (v3) is determined.

m1×v1+ m2×v2= (m1+m2)v3

Put the values;

150000 × 0.25+ 1000000×0.32= (150000+1000000)×v3

37500+ 320000= 1150000×v3

357500 = 1150000×v3

v3 = 0.311 m/s

Thus,

After one head-on elastic hit where the projectile is substantially more substantial than the target, the target particle's velocity will be nearly twice as fast as the projectile, but really the projectile's velocity will essentially be unaffected.

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The electric field due to these charges at some point a great distance from them is zero.

Electric field is a physical field created by a static electric charge or a changing electric charge. It is a vector field that exerts force on other charged particles. Electric fields are created when electric charges are separated, and the strength of the field is determined by the amount of charge and the distance from the charge.

This is because the electric field from an individual charge is inversely proportional to the square of the distance from it, and so the electric field from the two charges cancel each other out when the distance is greater than the separation between the electron and proton.

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After 2.00 seconds, the astronaut is moving at the speed of 0.67 m/s. The result is obtained by using the concept of Newton's second law.

The Newton's second law states that "The acceleration is directly proportional to the net force acting on an object and inversely proportional to the object's mass." It can be expressed as

a = ∑F/m

or

∑F = ma

Where

An astronaut moves after receiving a force. We have

Find the speed of the astronaut moving!

The force makes the astronaut moves from rest to a certain speed.

The speed can be calculated by the Newton's second law.

∑F = ma

∑F = m (v₁ - v₀)/t

30.0 = 90.0 (v₁ - 0)/2.00

60.0 = 90.0v₁

60.0/90.0 = v₁

v₁ = 2/3

v₁ = 0.67 m/s

Hence, the astronaut is moving at the speed of 0.67 m/s.

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The speed when they hit the street will be equal to each other.

Air resistance and gravity are the two fixed forces of nature which move on any object on Earth. For example, when a plane flies through the air, the air particles are pressing against the aeroplane, making it harder for the aircraft to move. When you see a feather fall, it is greatly affected by air resistance.

A force applied to all bodies on Earth is Weight ( W ), which is caused by Earth's gravity. If a body is free falling, its only acceleration is g , gravity. So gravity increases velocity. Both objects will show a change in their velocities because of gravity.

The velocity for both objects if one is thrown up and other is thrown down is same which is given by this formula:

where,

v= final velocity,

v₀= initial velocity,

h is the difference in height between building and street and g= acceleration due to gravity.

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A hamiltonian function representing an electron in the presence of a stationary positive point charge is

H = (p^2)/(2m) - (e^2)/(4πε_0r)

Generally, The Hamiltonian function representing an electron in the presence of a stationary positive point charge is given by:

H = kinetic energy + potential energy = (p^2)/(2m) - (e^2)/(4πε_0r)

where

Note that the first term represents the kinetic energy of the electron, and the second term represents the potential energy of the electron due to the attractive electrostatic force from the positive point charge.

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Answer: The mass on Moon will be 98. 1 kg.

Explanation:

As per the known fact, the mass is independent of acceleration due to gravity of planet.

The rightward directions she gives are as follows: 1. Move 400 meters to the northwest. 3. The wealth is hidden there, 700 meters to the east-southeast.

This means that anything is pushed toward the center of the earth, which causes the pulled object to accelerate by 9.8 meters per second as it "falls" to the earth. As a result, each second that such a body is dragged towards the earth, its velocity (speed with direction) increases by around 9.8 meters per second.

It should be remembered that gravitation is not a continuous force; gravity weakens the more you are from the center of the Earth. Since it fluctuates from 9.83 at the poles to 9.78 at the equator, it isn't even a consistent at the surface. Due to this, we utilize an average value of 9.8.

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Answer:

To gradually increase blood flow to the body

Yes, the velocity of the ball has changed as it changed its direction from hitting the wall and after it struck the wall.

Speed is a scalar which means it has magnitude but not the direction. Velocity, on the other hand, is a vector with both magnitude and a direction. As the speed of two cars may be the same, if they are heading to different directions, then their velocity are not identical.

The velocity of he ball has changed. Let's call that the initial direction positive, when the ball was going towards the wall, its velocity is positive +V. But when it bounces directly back, the direction is now is negative -V. The direction of the velocity has changed, even though the magnitude has not.

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The force of gravity the moon exerts on you is greater than the force of gravity you exert on the moon.

The force of gravity is a fundamental pressure of nature that acts between two gadgets with mass. It's miles the pressure that attracts  objects toward every other, and its energy is proportional to the mass of the gadgets and the space among them. The pressure of gravity is liable for the motion of planets and different celestial gadgets, as well as for maintaining items on the floor. It turned into first described by way of Sir Isaac Newton in his laws of motion and normal gravitation, which stated that every item inside the universe attracts each different item with a pressure proportional to the product of their masses and inversely proportional to the rectangular of the distance between them.

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The force the moon exerts on you is greater.

Gravity is a force of attraction between two objects in space that is proportional to the masses of the objects and inversely proportional to the square of the distance between them. It is the force that holds planets in orbit around stars and is what causes objects to fall to the ground when dropped. On Earth, the force of gravity is what gives weight to objects and what keeps us anchored to the surface. The strength of the gravitational force is determined by the mass of the objects and the distance between them, with more massive objects having a stronger gravitational pull.

The force of gravity is the force with which a celestial body attracts objects toward its center. The force of gravity is proportional to the mass of the object and inversely proportional to the square of the distance between the objects. The force of gravity acts as the source of the weight of objects. The force of gravity is responsible for holding objects in orbit around the earth and other celestial bodies. The most well-known example of the force of gravity is the attraction between the earth and moon, which causes the tides.

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The velocity with which the ball left the ground when it is dropped from a tall building is calculated to be 25.82 m/s.

Height to which a ball bounces back s = 34 m

From the equations of kinematics, we know, the relation connecting height, velocities and acceleration as,

v² - u² = 2 a s

where, v is the final velocity

u is the initial velocity

a is the acceleration

s is the height travelled

Here, u = 0 and a is the acceleration due to gravity

v² = 2 × 9.8 × 34

v² = 666.4

v = 25.82 m/s

Thus, the velocity with which the ball left the ground is calculated to be 25.82 m/s.

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Answer:

1) [tex]t=4.16s[/tex]

2) [tex]s=44.10m[/tex]

3) [tex]v_{final}=40.84\frac{m}{s}[/tex]

Explanation:

a) How long till it hits the ground?

Since the person threw the ball perfectly horizontal, the ball has 0 vertical velocity at the start. In fact, it takes the same time for the ball to reach the ground if they dropped the ball instead of throwing. The acceleration in a vertical drop is gravity ([tex]a=9.81\frac{m}{s^2}[/tex])

Basically, we'll solve first part as if he just dropped the ball.

Use this linear motion formula:

[tex]s=v_{inital}(t_{final} -t_{initial})+1/2a(t_{final}-t_{inital})^2[/tex]

Since [tex]v_{initial} =0[/tex] we can remove that part from equation:

[tex]s=1/2a(t)^2[/tex]

[tex]85=1/2*9.81(t)^2[/tex] Plug and solve

[tex]170=9.81(t)^2[/tex]

[tex]17.33=t^2[/tex]

[tex]t=4.16s[/tex]

b) How far away does it land?

We will use the same formula above for horizontal motion.

[tex]s=v_{inital}(t_{final} -t_{initial})+1/2a(t_{final}-t_{inital})^2[/tex]

[tex]s=v(t)+0[/tex]  (Remove the last part since [tex]a=0[/tex])

[tex]s=10.6(4.16)[/tex]

[tex]s=44.096m[/tex]

c) How fast was it traveling vertically at the end?

Use this other linear motion formula for this step. s=85m (height of building).

[tex]v_{final} ^2-v_{initial} ^2=2as[/tex]

[tex]v_{final} ^2-0^2=2(9.81)*(85)[/tex] Started with 0 vertical velocity.

[tex]v_{final} ^2=1667.7[/tex]

[tex]v_{final}=40.837m/s[/tex]

According to the question of speed, a) 16.05 seconds does the ball hit the ground, b) 169.33 m far from the building will it land, c) 37.68 m/s is the velocity of the ball just before it hits the ground.

What is speed?
Speed is the rate at which something moves or an object's rate of motion. It can be measured in metres per second, kilometres per hour, and miles per hour, and is often used to describe the motion of objects, such as vehicles, animals, or natural phenomena.

a. The time it takes for the ball to hit the ground is given by the equation t = (2×h)/v, where h is the height of the building (85 m) and v is the initial velocity of the ball (10.6 m/s). Plugging in the given values, we get t = (2×85)/10.6 = 16.05 seconds.

b. The distance from the building at which the ball will land is found using the equation x = vt, where v is the initial velocity (10.6 m/s) and t is the time it takes for the ball to hit the ground (16.05 seconds). Plugging in the given values, we get x = 10.6×16.05 = 169.33 m.

c. The velocity of the ball just before it hits the ground is determined by the equation v = √(2gh), where g is the acceleration due to gravity (9.8 m/s2) and h is the height of the building (85 m). Plugging in the given values, we get v = √(2×9.8×85) = 37.68 m/s. This is the velocity of the ball just before it impacts the ground.

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Geosynchronous satellite makes a round around the earth in 29.93 hours. It makes a difference of 36000 km difference in the altitude.

Geosynchronous satellites are those that remains stationery with respect to a place. This is because their time period to complete a cycle is 23.93 hours, that is exactly the same as the rotation period of the earth. So the satellite appears stationery. The velocity of the geosynchronous satellite around the earth is 3.07 km/s or 3070 m/s.

GMm/(R+h)² = mv²/(R+h)

GM/v² = (R+h)²

Where R is the radius of the earth = 6.37 × 10⁶ m, h is the altitude of the satellite above the earth, and M is the mass of the earth that is 6 × 10²⁴ kg, G = 6.67 × 10⁻¹¹ Nm²/kg²

(6.67 × 10⁻¹¹ ×6 × 10²⁴)/(3070)² = (R+h)

(R+h) = 42461989 m

6.37 × 10⁶ + h = 42461989

h = 42461989 - 6.37 × 10⁶

h = 36.09 × 10⁶  m

h = 36000 km.

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The heat required would be Q = 7.0 g/28 g/mol * 20.8 J/molK * (2T - T) = 544 J.

Heat is the transfer of energy from one body or system to another due to the difference in their temperatures. Heat is commonly transferred through thermal conduction, convection, radiation, or when two bodies with different temperatures come into direct contact.

The heat required for a process at constant pressure is greater than the heat required for a process at constant volume. This is because when a gas is heated at constant pressure, work is done to push the piston outward, so more energy is required.

To double the volume and temperature at constant pressure, the heat required would be equal to the change in internal energy of the system,
which can be calculated using the equation Q = nCvΔT,
where n is the number of moles of gas,
Cv is the molar heat capacity,
and ΔT is the change in temperature.
In this case, the molar heat capacity of nitrogen gas is 20.8 J/molK,
So the heat required would be Q = 7.0 g/28 g/mol * 20.8 J/molK * (2T - T) = 544 J.

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The minimum size of the snowshoes needed to enable her to walk without sinking will be 1.37 m².

Assumption:

(i) Her weight is uniformly distributed on the imprint area

(ii) the weight of the shoes is negligible

Now, given that mass of women, m = 70 kg

For a pressure of 0.5 kPa on the snow, the imprint area of one shoe must be:

A = W/P

here, W = mg = 70 kg . 9.81 m/s² = 70x9.81 N

P = 0.5 kPa = 0.5 x 1000 N/m²

so, A = [tex]\frac{70x9.81 N}{0.5(1000)N/m^2}[/tex]

or A = 1.37 m²

Therefore, the minimum size of the snowshoes needed to enable her to walk without sinking will be 1.37 m².

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