A rod of length 35.50 cm has linear density (mass per length) given by λ = 50.0 + 23.0x where x is the distance from one end, and λ is measured in grams/meter. (a) What is its mass? g (b) How far from the x = 0 end is its center of mass? m

Answer:

Gold nugget diameter    22,24 cm

Silver nugget price   38860  $

Explanation:  

Gold price    1400  $ /ou            1  ounce  = 31.1035 grs

so  1400 /31.1035

Gold price is 45,01   $/grs.

If a nugget worth   5000000 $  then  5000000/ 45.01

a nugget mass  :  111086,43 grs

Now gold density  is  d = 19.3 grs/cm³

And she volume is  V = 4/*π*r³

d = m/V         V = m/d           V  =   111086.43/19.3    cm³

V = 5755,77 cm³

Now V of the sphere is  V =  5755,77 = 4/3*π*r³

r³  =3*5755,77 / 4π        r³  = 1374,79

r  =  11.12 cm      2r  =  22,24  =  Φ (sphere diameter)

B)  d (silver)  =  m/V       m = d*V

V = 5755,77 cm³     The same size the same volume

m =  10,5 * 5755,77 [grs/cm³ * cm³]       m  = 60435,59 grs

Silver nugget worth  :

20  $ /ou         20/31.1035  =   0.643  $ /grs

Price   0,643 *  60435,59  =  38860  $

Answer: 0.58

Explanation:

First we need to get the acceleration of the body using equation of motion

v²=u²-2as

v is the final velocity

u is the initial velocity

a is acceleration

s is the distance moved

0²=9²-2a(2.6)

-81=-5.2a

a=81/5.2

a= 15.6m/s²

Angle of inclination =30°

To get the coefficient of friction, we use the formula

Ff =nR

Ff is frictional force

n is coefficient of friction

R is normal reaction

n = Ff/R = Wsin30°/Wcos30°

n = tan30°

n = 0.58

Final answer:

The linear velocity of the space telescope is about 17,193.2 miles per hour when rounded to the nearest tenth. This is calculated using the orbit radius of 4340 miles and the orbital period of 1.5833 hours.

Explanation:

To calculate the linear velocity of a space telescope traveling around Earth, we need to use the formula v = 2πr / T, where v is the linear velocity, r is the radius of the orbit, and T is the orbital period. To find the orbit radius, we add Earth's radius and the altitude of the telescope above Earth's surface: r = 3960 miles + 380 miles = 4340 miles.

Next, we convert the orbital period from minutes to hours. There are 60 minutes in an hour, so T = 95 minutes / 60 minutes/hour = 1.5833 hours. We can then plug the radius and period into the formula to find the linear velocity: v = 2 x π x 4340 miles / 1.5833 hours = 17,193 miles/hour. When rounded to the nearest tenth, the linear velocity is approximately 17,193.2 miles per hour.

Answer:

Yes

Explanation:

Gravity and forces form the axle (external forces) do not cause forces that tend to cause rotation around the turntable's axle.

Answer:

Molar mass due to different atomic masses

Explanation:

Two gases that have the same volume, pressure and gases have the same number of moles, as we can deduce from the ideal gas equation. So the gases will have the same number of moles of gases but they can have densities due to the fact that they have different molar masses due to the fact that they have different atomic masses. So one gas will be heavier than the other, for the same volume.

Answer:

C. Both Technicians A and B

Explanation:

To loosen a fastener immediately especially if it is a rusted one we can follow these steps.

1. Tap the sides of the fastener so that the rust particle fall off.

2. These rust particles can be brushed off.

3. Spray the fastener with the penetrating oil.

4. Again tap the sides with a hammer to let the oil penetrate the inter-locked parts (threads in case of a nut and bolt).

5. Loosen the fastener after oil has penetrated.

Note: It should be kept in consideration that spraying alone won't do the job, tapping is essential to let the oil penetrate deep in to free the rusted parts.

Answer:

B. the stars of spectral type A and F are considered reasonably to have habitable planets but much less likely to have planets with complex plant - or animal - like life.

Explanation:

The appropriate spectral range for habitable stars is considered to be "late F" or "G", to "mid-K" or even late "A". This corresponds to temperatures of a little more than 7,000 K down to a little less than 4,000 K (6,700 °C to 3,700 °C); the Sun, a G2 star at 5,777 K, is well within these bounds. "Middle-class" stars (late A, late F, G , mid K )of this sort have a number of characteristics considered important to planetary habitability:

• They live at least a few billion years, allowing life a chance to evolve. More luminous main-sequence stars of the "O", "B", and "A" classes usually live less than a billion years and in exceptional cases less than 10 million.

• They emit enough high-frequency ultraviolet radiation to trigger important atmospheric dynamics such as ozone formation, but not so much that ionisation destroys incipient life.

• They emit sufficient radiation at wavelengths conducive to photosynthesis.

• Liquid water may exist on the surface of planets orbiting them at a distance that does not induce tidal locking.

Thus , the stars of spectral type A and F are considered reasonably to have habitable planets but much less likely to have planets with complex plant - or animak - like life.

Answer:

(b) The electrons, because they have the smaller momentum and, hence, the larger de Broglie wavelength

Explanation:

de Broglie wavelength λ = h / m v

Since both electrons and protons have same velocity , momentum mv will be less for electrons because mass of electron is less .

for electron , momentum is less so  . Therefore de Broglie wavelength λ will be more for electrons .

Amount of diffraction that is angle of diffraction is proportional to λ

Therefore electrons having greater de Broglie wavelength will show greater diffraction.

Answer:

Covalent bonding

Explanation:

Covalent bonding is the type of bonding found in all molecular substances much as water, carbon dioxide or methane. Unlike ionic bonding which is found in ionic substances, covalent bonding involves sharing, not transfer, of electrons between the bonding atoms to form molecules.

Answer:

so throwers new velocity = 2.18032m/s

so catchers new velocity = 0.02577m/s

Explanation:

Directly by conservation of momentum we can write

[tex]m_1u_1+m_2u_2= m_1v_1+m_2v_2[/tex]

let x be the thrower's new velocity

(70+0.042)×2.2 + 57×0 = 70× x +0.042×35 +57×0

x = 2.18032m/s

so the velocity of 70 kg man = 2.18032m/s

so throwers new velocity = 2.18032m/s

now again by conservation of momentum

0.042×35 = (57+0.042) ×y

y = 0.02577m/s

so catchers new velocity = 0.02577m/s

Answer:

(A) COP = 2.64

(B) rate of heat absorption= 1.9637 kW

Explanation:

mass flow rate (m) = 0.018 kg/s

work input (Win) = 1.2kW

inlet pressure (P1) = 800kPa

inlet temperature (T1) = 35 degree Celsius

h1 = 271.24 KJ/Kg

outlet pressure (P2) = 800 kPa

outlet temperature (T2) = ?

entalphy (h2) = 95.48 KJ/Kg

The entalphies are gotten from tables for refrigerant 134a at the temperatures and pressures above

(A) COP = Qh ÷ Win

     where Qh  = m(h1 -h2) from the energy balance equation

     Qh = 0.018 ( 271.24 - 95.48 ) = 3.1637 kW

     COP = 3.1637 ÷ 1.2 = 2.64

(B) rate of heat absorption = Qh - Win

    = 3.1637 - 1.2 = 1.9637 kW

The COP of a heat pump is calculated by using the formula COP = Q_H/W, where Q_H is the heat delivered to the house and W is the work done. Utilizing the specific enthalpies and flow rate, Q_H can be calculated. Subsequently, the rate of heat absorption from the outside can be deduced using Q_L = Q_H - W.

The thermal efficiency or COP (Coefficient of Performance) of the heat pump can be calculated using the equation: COP = Q_H/W where Q_H is the heat delivered to the house and W is the work input. In this case, since the fluid leaves the condenser as a saturated liquid, Q_H = m_dot*(h_1 - h_2), where h_1 and h_2 are the specific enthalpies at the state 1 and state 2 and m_dot is the mass flow rate of refrigerant.

From the saturated liquid tables, we know that the specific enthalpy h_2 = 257 kJ/kg for Refrigerant-134a at 800 kPa. Thus, Q_H can be calculated and this value (in kW) can be used to calculate COP.

Then, to answer part (b), the rate of heat absorption from the outside air can be calculated using the equation Q_L = Q_H - W. Q_L is the rate of heat absorption, Q_H is the heat delivered to the house and W is the power absorbed by the compressor.

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Answer:

1.07 m

Explanation:

x = Compression of the spring

k = Spring constant = 53 N/m

Initial length = 18 cm

P = Kinetic energy

K = Kinetic energy

At the lowest point of the mass the energy conservation is as follows

[tex]P_{ig}+P_{is}+K_i=P_{fg}+P_{fs}+K_f\\\Rightarrow mgx+0+0=mgx+\frac{1}{2}kx^2\\\Rightarrow x=\frac{2mg}{k}\\\Rightarrow x=\frac{2\times 2.4\times 9.81}{53}\\\Rightarrow x=0.89\ m[/tex]

At its lowest position the mark on the ruler will be

[tex]x_f=0.18+0.89\\\Rightarrow x_f=1.07\ m[/tex]

The spring line will end up at 1.07 m

In this scenario, when a 2.4 kg mass is attached to a spring, the spring gets displaced due to the force exerted by the mass due to gravity. The displacement can be calculated using Hooke's Law (F = kx), resulting in a mark of 62.4 cm on the ruler when the mass is at its lowest position.

The phenomenon described in this question is related to Hooke's Law of Physics, which states that the force required to extend or compress a spring by a distance is proportional to that distance. The force exerted by the spring is measured in Newtons (N) and is given by the equation F = kx, where k is the spring constant and x is the distance the spring is stretched or compressed.

In this case, when the 2.4 kg mass is attached to the spring, it will exert a force due to gravity which is equal to the mass times the acceleration due to gravity (g = 9.8 m/s²), therefore F = m*g = 2.4kg * 9.8m/s² = 23.52 N. The spring reacts to this force and gets displaced, which can be calculated using x = F/k = 23.52N / 53N/m = 0.444 m or 44.4 cm. Therefore, with the mass attached, the bottom of the spring would fall to 18cm + 44.4 cm = 62.4 cm on the ruler.

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Answer:

Running or Jogging

Running and jogging are both great options for aerobic conditioning. Whether you run at the gym or outside, you are in control of setting the intensity of your workout. When aiming to build muscle mass, you can add more resistance or jog at an incline, along with increasing your speed.

Explanation:

Answer:

Running

Jogging

Yoga

Explanation:

Running Jogging and yoga best describes aerobic exercise plan. Aerobic exercises are those where cardiovascular conditioning happen it can be swimming, cycling ,running, jogging etc. aerobic exercise is good for health as it reduces risk of:- obesity, high blood pressure type 2, diabetes, metabolic syndrome , strokes and some type of cancer too can be avoided by doing aerobic exercise.

Answer: To form a cloud, the air that rises must cool to the point where some of the water vapor molecules "clump together" at a faster pace than they are pulled apart by their thermal energy. These molecules then condense to form the clouds and water droplets.

We can see here that Cloud formation in the atmosphere requires two main conditions: the presence of water vapor and the cooling of air.

The atmosphere is a layer of gases that surrounds a planet or celestial body, held in place by gravity. On Earth, the atmosphere is the layer of gases that envelops the planet and sustains life. It plays a crucial role in protecting and supporting life on Earth by providing essential elements, regulating temperature, and facilitating various atmospheric processes.

Clouds play a crucial role in the Earth's climate system by reflecting sunlight back into space (resulting in cooling) and trapping heat radiated from the Earth's surface (resulting in warming).

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The velocity of the ball is 7 m/s

Explanation:

The motion of the ball is a free fall motion, so it means that the ball falls down under the effect of the force of gravity only. Therefore, it has a constant acceleration (acceleration of gravity, g), and we can use the following suvat equation:

[tex]v^2-u^2=2as[/tex]

where

v is the final velocity

u is the initial velocity

a is the acceleration

s is the displacement

For the ball in this problem, we have:

u = 0 (initial velocity, the ball is dropped from rest)

[tex]a=g=9.8 m/s^2[/tex] (acceleration of gravity)

s = 2.5 m (vertical displacement)

Solving for v, we find the velocity at which the ball hits the concrete surface:

[tex]v=\sqrt{u^2+2as}=\sqrt{0+2(9.8)(2.5)}=7 m/s[/tex]

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Answer:

a) The screen should be located at 1.08 meters

b) The width of the central maximum is 1.7 mm

c) See figure below.

Explanation:

a) This is a single slit diffraction problem, the equation that describes this kind of phenomenon is:

[tex]a\sin\theta=m\lambda [/tex] (1)

Because we’re interested in a minimum near the center of the screen, we can use the approximation [tex] \sin\theta\approx\tan\theta=\frac{y}{x} [/tex]

So equation (1) is now:

[tex]a\frac{y}{x}=m\lambda [/tex] (2)

Solving (2) for x:

[tex] x=\frac{ay}{m\lambda}=\frac{(0.75\times10^{-3})(0.85\times10^{-3})}{1(587.5\times10^{-9})}\approx1.08m [/tex]

b) As you can see on the figure below a maximum is approximately between the two adjacent minimums, because the diffraction pattern is approximately symmetric respect the center of the screen the width of the central maximum is 2*0.850mm = 1.7 mm.

Answer:

- Elevated temperatures.

- Elevated pressures.

Explanation:

In the manufacture of plastic products are used:

Raw material (pellets) which are the monomers that promote the chemical reaction.

To these are added the charges, in order to reduce the cost of the final product and improve some properties. These charges can be fiberglass, paper, metal structures.

Additives are also added whose mission is to improve or achieve certain properties, such as reducing friction, reducing chemical degradation, increasing electrical conductivity, coloring the product, and all this happens in the presence of a catalyst that is responsible for initiating and accelerating the chemical reaction process.

There are different methods of production of plastics, one of the most frequent is by injection.

Injection is a process that is carried out on machines similar to extrusion machines, in which the spindle, in addition to rotating, has an axial displacement.

In the injection, once the mold is filled, it is separated from the nozzle of the machine, breaking the feed channel. After a certain time, the piece already cooled is demoulded.

High pressures and temperatures are necessary, but parts of good finish and at high production speeds are obtained

The correct answer is: Elevated temperatures.

During fabrication processes, polymeric materials are often subjected to elevated temperatures. This is because many polymers are thermoplastic, meaning they soften and can be reshaped when heated. The elevated temperatures allow the polymer chains to move more freely, enabling the material to be molded, extruded, or otherwise formed into the desired shape or structure.

While ambient temperature and pressure can also affect polymeric materials, the key condition for shaping and fabricating these materials is typically elevated temperature. Ambient temperature is usually not sufficient to induce the necessary molecular mobility for fabrication. Ambient pressure is generally constant and does not play a significant role in the fabrication process unless specific pressure conditions are required for certain molding techniques, such as injection molding or compression molding, where controlled pressure is applied to ensure the polymer fills the mold properly.

The intensity of the sound will be B. Nine times lower

Explanation:

The intensity of a sound follows an inverse square law, which means that it is inversely proportional to the square of the distance from the source:

[tex]I\propto \frac{1}{r^2}[/tex]

where

I is the intensity

r is the distance from the source

In this problem, the siund has an intensity of I when the receiver is placed at a distance r from the source.

Later, the receiver is placed three times farther away, so the new distance is

r' = 3r

Therefore, the new intensity of the sound will be:

[tex]I'\propto \frac{1}{r'^2}=\frac{1}{(3r)^2}= \frac{1}{9} (\frac{1}{r^2})= \frac{1}{9}I[/tex]

Therefore, the intensity of the sound received will be nine times lower.

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Answer:     B. Nine times lower

Explanation:

Answer:

None of the given options

Explanation:

If the angular speed is constant, there is no angular acceleration:

α=0

If there is no angular acceleration, tangential acceleration will also be 0.

Centripetal acceleration, on the other hand, will be:

[tex]ac =\omega^2*R[/tex]  (Different to 0)

Answer:

8000

Explanation:

cause in the problem we dont have any ext Forces we know that the momentum of system is constant.

Fext=0

P1 + P2 = P1' + P2'

P2 = 0

5000 = -3000 + P2'

P2' = 5000+3000 = 8000

Answer:

x = 0.6034 m

Explanation:

Given

L = 5 m

Wplank = 225 N

Wman = 522 N

d = 1.1 m

x = ?

We have to take sum of torques about the right support point.  If the board is just about to tip, the normal force from the left support will be going to zero.  So the only torques come from the weight of the plank and the weight of the man.

∑τ = 0  ⇒     τ₁ + τ₂ = 0  

Torque come from the weight of the plank = τ₁

Torque come from the weight of the man = τ₂

⇒  τ₁ = + (5 - 1.1)*(225/5)*((5 - 1.1)/2) - (1.1)*(225/5)*((1.1)/2) = 315 N-m (counterclockwise)

⇒  τ₂ = Wman*x = 522 N*x   (clockwise)

then

τ₁ + τ₂ = (315 N-m) + (- 522 N*x) = 0

⇒  x = 0.6034 m

The frequency of the yellow light is [tex]5.17\cdot 10^{14}Hz[/tex]

Explanation:

The relationship between wavelength, frequency and speed of a wave is given by the wave equation:

[tex]v = f \lambda[/tex]

where

v is the speed of the wave

f is the frequency

[tex]\lambda[/tex] is the wavelength

For the yellow light in this problem, we have:

[tex]v=1.97\cdot 10^8 m/s[/tex] is the speed

[tex]\lambda=3.81\cdot 10^{-7} m[/tex] is the wavelength

Solving for f, we find its frequency:

[tex]f=\frac{v}{\lambda}=\frac{1.97\cdot 10^8}{3.81\cdot 10^{-7}}=5.17\cdot 10^{14}Hz[/tex]

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The frequency of the yellow light in the glass block is [tex]5.17 \times 10^{14}Hz[/tex]

Yellow light travels through a certain glass block at a speed of 1.97 × 108 m/s. The wavelength of the light in this particular type of glass is 3.81 × 10−7 m (381 nm).

[tex]= 1.97 \times 10^8 \div 3.81 \times 10^{-7}\\\\= 5.17 \times 10^{14}Hz[/tex]

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Answer:

B. Color perception is achieved by activation of various combinations between the tree cone types.

Explanation:

Human eye have only three photo receptor ( three wavelength) but they can see several thousands of shades of color because color perception is gained by combination of these three wave length cone types ( RED, BLUE AND GREEN) into various combinations. Our retina have two types of cell:- cone cells and cylindrical cells. Cone cells are responsible for the identification of color.

Answer:

Explanation:

Relation between Celsius and Kelvin is

K = C + 273

Relation between Kelvin and Fahrenheit is

[tex]\frac{K-273}{100}=\frac{F -32}{180}[/tex]

(a) 379 K

Relation between Celsius and Kelvin is

K = C + 273

So, C = K - 273 = 379 - 273 = 106

Thus, 379 K = 106°C.

(b) 379 K

Relation between Kelvin and Fahrenheit is

[tex]\frac{K-273}{100}=\frac{F -32}{180}[/tex]

[tex]\frac{379-273}{100}=\frac{F -32}{180}[/tex]

F = 222.8°F

Thus, 379 K = 222.8°F

(c) 1.04 x 10^2 K = 104 K

Relation between Celsius and Kelvin is

K = C + 273

So, C = K - 273 = 104 - 273 = -169

Thus, 104 K = - 169°C.

(d) 1.04 x 10^2 K = 104 K

Relation between Kelvin and Fahrenheit is

[tex]\frac{K-273}{100}=\frac{F -32}{180}[/tex]

[tex]\frac{104-273}{100}=\frac{F -32}{180}[/tex]

F =- 272.2°F

Thus, 104 K = - 272.2°F

Answer:

option A

Explanation:

The correct answer is option A

People fighting forest fire carry emergency tent which has a shiny outer surface because the radiation of the heat which is downward toward firefighter the aluminium tents reflects the heat from the fire.

Aluminium Reflects 95 % of the infrared heat that hit the shiny surface of aluminium i.e. it is used by the firefighter to prevent from the heat radiation.

Final answer:

Emergency tents with shiny aluminum outer surfaces protect firefighters from heat primarily by reflecting infrared radiation. Convection plays a lesser role as hot air rises, and conduction is minimal. Radiative heat, the main form of heat transfer from fire, is what the tents are designed to protect against.

Explanation:

The reason emergency tents with shiny aluminum outer surfaces help firefighters when they lie under them to block heat from burning trees overhead is due to the tent's ability to reflect infrared radiation. Heat from fires is primarily transferred through radiation, particularly infrared radiation, which the shiny aluminum surface is effective at reflecting away. This reflection helps to protect the firefighter by reducing the amount of heat that reaches them. Convection plays a smaller role in transferring heat downward in this scenario, since hot air tends to rise, and conduction is negligibly slow here, especially from the fire to the tent. Therefore, the tents are designed to reflect the intense radiative heat that a fire emits, which is the main mechanism at play in this scenario for heat transfer.

Final answer:

The piano tuner should loosen the piano string after hearing an increase from three beats per second to six beats per second upon tightening the string, as this indicates the string's frequency was adjusted away from the tuning fork's frequency.

Explanation:

When a piano tuner hears beats, it indicates that there is a frequency difference between a tuning fork and the piano string that is being compared. Initially, the tuner hears three beats per second, which means the frequency of the piano string is either slightly higher or lower than that of the tuning fork. After tightening the string, the number of beats per second increases to six. This indicates that the frequency of the string has moved further away from the frequency of the tuning fork.

The fact that the beats increased after tightening the string implies that the tuner has adjusted the frequency of the piano string in the wrong direction. Since the goal is to eliminate the beats entirely by matching frequencies, the tuner should loosen the string to reduce the frequency instead of tightening it further.

Answer:

Time, t = 2 minutes

Explanation:

Given that,

Length of Duplain st. d = 300 m = 0.3 km

If keith is strolling east from Baron at an average velocity of, v = 3 km/hr

Sue is power-walking west from Burkey at an average velocity of, v' =  6 km/hr

To find,

How long will it take them to meet ?

Solution,

When both objects are travelling in opposite direction, then the total speed is given by :

V = v + v'

V = 3 km/hr + 6 km/hr

V = 9 km/hr

Let t is the time taken will it take them to meet. It can be calculated as :

[tex]t=\dfrac{d}{V}[/tex]

[tex]t=\dfrac{0.3\ km}{9\ km/hr}[/tex]

t = 0.033 hour

or

t = 1.98 minutes

i.e. t = 2 minutes

So, they will take 2 minutes to meet. Hence, this is the required solution.

Answer:

x = 7.62 m

Explanation:

First we need to calculate the weight of the rocket:

W  = mg

we will use the gravity as 9.8 m/s². We have the mass (500 g or 0.5 kg) so the weight is:  

W  = 0.5 * 9.8 = 4.9 N

We know that the rocket exerts a force of 8 N. And from that force, we also know that the Weight is exerting a force of 4.9. From here, we can calculate the acceleration of the rocket:

F - W = m*a

a = F - W/m

Solving for a:

a = (8 - 4.9) / 0.5

a = 6.2 m/s²

As the rocket is accelerating in an upward direction, we can calculate the distance it reached, assuming that the innitial speed of the rocket is 0. so, using the following expression we will calculate the time which the rocket took to blast off:            

y = vo*t + 1/2 at²

y = 1/2at²

Solving for t:

t = √2y/a

t = √2 * 20 / 6.2

t = √6.45 = 2.54 s

Now that we have the time, we can calculate the horizontal distance:

x = V*t

Solving for x:

x = 3 * 2.54 = 7.62 m            

Answer:

Angular speed will reach 6.833rad/s before the coin starts slipping

Explanation:

There is no question but I'll asume the common one: Calculate the speed of the turntable before the coin starts slipping.

With a sum of forces:

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

[tex]Ff=m*V^2/R[/tex]

At this point, friction force is maximum, so:

[tex]\mu*N=m*V^2/R[/tex]

[tex]\mu*m*g=m*V^2/R[/tex]

Solving for V:

[tex]V=\sqrt{\mu*g*R}[/tex]

V=1.025 m/s

The angular speed of the turntable will be:

ω = V/R = 6.833 rad/s   This is the maximum speed it can reach before the coin starts slipping.

Answer:

Rate of plane in still air = P = W (t1 +t2)/ (t1-t2)

Rate of wind in still air = W = P (t1 - t2)/(t1 + t2)

Explanation:

Assuming speed of plane are the same on both trips

Rate (D/t1) = (P-W).... EQU 1 going from city a to b

Rate (D/t2) = (P +W)...Equ2 going back to city a

Where t1 is not equal to t2

Where D=distance between two cities

P &W are the speed of plane and wind

t1 &t2 = time taken for travel

Equ 1 & equ 2 becomes

D = ( P - W ) t1.. equ3

D = ( P + W ) t2 equa4

Equating equ 3 and 4

Pt1 - Wt1 = Pt2 +Wt2

P ( t1 - t2) = W ( t1 + t2)

Rate of plane in still air = P = W (t1 +t2)/ (t1- t2)

Rate of wind in still air = W = P (t1 - t2)/(t1 + t2)