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1 month ago

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An airplane cruises at 850 km/h relative to the air. It is flying from Denver, Colorado, due west to Reno, Nevada, a distance of

1200 km, and will then return. There is a steady 90km/h wind blowing to the east.

1 answer:

Yuliya22 [3.3K]1 month ago

8 0

Answer:

the difference in flight duration= 0.3023 hours

Explanation:

The question details are lacking, but I located it within your textbook.

Aircraft speed = 850 km/h

Wind speed against the aircraft = 90 km/h

As a result, the effective speed flying west = 850 - 90 = 760 km/hr

Distance traveled = 1200 km

time required = distance/speed = 1200/760 = 1.5789 hours

Returning, wind speed complements aircraft speed, thus

net speed for return journey = 850 + 90 = 940 km/hr

time taken for return = 1200/940 = 1.2765 hours

Consequently, the difference in flight duration= 1.5789 - 1.2765 = 0.3023 hours

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Suppose that A’, B’ and C’ are at rest in frame S’, which moves with respect to S at speed v in the +x direction. Let B’ be loca

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Response:

1) An observer in B 'perceives the two events occurring at the same time

2) Observer B recognizes that the events happen at different times

3) Δt = Δt₀ /√ (1 + v²/c²)

Clarification:

This scenario illustrates the concept of simultaneity in special relativity. It is important to keep in mind that light's speed remains constant across all inertial frames

1) Since the events are stationary within the frame S ', they propagate at the constant speed of light, resulting in them reaching observation point B'—located equidistantly between both events—simultaneously

Thus, an observer in B 'observes the two events occurring at the same time

2) For an observer B situated within frame S attached to the Earth, both events at A and B appear to take place at the same moment. However, the event at A covers a shorter distance, while the event at B travels a longer distance, since frame S 'is in motion at velocity + v. Hence, with a constant speed, the event covering the lesser distance is perceived first.

Consequently, observer B perceives that the events do not occur simultaneously

3) Let's determine the timing for each event

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where t₀ represents the time in the S' frame, which remains at rest for the events

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1 month ago

A 1.97-pF capacitor with a plate area of 5.86 cm2 and separation between the plates of 2.63 mm is connected to a 9.0-V battery a

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If the plate separation is modified after the battery is disconnected, the updated distance between plates is 9.21 mm

If changes are made while the battery remains connected, the new separation becomes 0.11 mm

The capacitance for an air-filled parallel plate capacitor can be expressed as:

$C=\frac{\epsilon_0A}{d}$

In this equation, $\epsilon_0$ refers to the permittivity of free space, A stands for the plate area, and D represents the separation distance.

Thus,

$C \alpha \frac{1}{d}$ .......(1)

Therefore, should the distance between the plates shift from d₁ to d₂, the capacitance ratio in both scenarios can be represented as:

$\frac{C_1}{C_2} =\frac{d_2}{d_1}$ ......(2)

Scenario (i)

When the capacitor is fully charged and then disconnected from the battery before adjusting the plate distance, the charge will remain steady while the capacitance varies.

The initial energy E₁ stored in the capacitor can be expressed as:

$E_1=\frac{Q^2}{2C_1}$ ......(3)

Once the separation changes to d₂, capacitance becomes C₂, but the charge Q remains unchanged.

Thus,

$E_2=\frac{Q^2}{2C_2}$ ......(4)

By dividing equation (4) by (3),

$\frac{E_2}{E_1} =\frac{C_1}{C_2}$

According to equation (2),

$\frac{E_2}{E_1} =\frac{C_1}{C_2}=\frac{d_2}{d_1}$

This results in a 3.5 fold increase in energy.

$\frac{E_2}{E_1} =\frac{d_2}{d_1}=3.5\\ d_2=3.5*2.63 mm\\ =9.205 mm=9.21 mm$

Scenario (2)

If the capacitor is kept connected to the power source, the voltage V across the plates will remain unchanged.

The initial energy is described as

$E_1=\frac{1}{2} C_1V^2$ ......(5)

The final energy when the plate separation transitions to d₂ can be written as:

$E_2=\frac{1}{2} C_2V^2$ .....(6)

Referencing equations (5) and (6)

$\frac{E_2}{E_1} =\frac{C_2}{C_1}$

From equation (2),

$\frac{E_2}{E_1} =\frac{C_2}{C_1}=\frac{d_1}{d_2}$

Thus, in this particular scenario,

$\frac{E_2}{E_1} =\frac{d_1}{d_2}\\d_2=\frac{d_1}{3.5} \\ =\frac{2.63 mm}{3.5} \\ =0.109 mm=0.11 mm$

Therefore,

Adjusting plate separation after battery disconnection yields 9.21 mm

If modified while connected, the new separation measures 0.11 mm

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The resulting motion can be determined using the Pythagorean theorem, as the two components (north and east) are at right angles. To find the direction, trigonometry is applied, yielding Ф=arctan(3.8/12)=17.57° north of east.

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1 month ago

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A wire has an electric field of 6.2 V/m and carries a current density of 2.4 x 108 A/m2. What is its resistivity

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Response:

The resistivity can be expressed as $\rho = 2.5 *10^{-8} \ \Omega \cdot m$

Clarification:

According to the information provided,

The value of the electric field measures $E = 6.2 V/m$

The density of current is given as $J = 2.4 *10^{8} \ A/m^2$

Typically, resistivity is represented in mathematical terms as

$\rho = \frac{E}{J}$

by inserting values

$\rho = \frac{6.2}{2.4 *10^{8}}$

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A wildlife researcher is tracking a flock of geese. The geese fly 4.0 km due west, then turn toward the north by 40° and fly ano

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Answer:

(a). The distance traveled is 7.06 km towards the west.

(b). Their displacement magnitude is 7.51 km.

Explanation:

The information given states that,

The geese initially move 4.0 km directly west, then alter course to the north at a 40° angle, covering an additional 4.0 km.

Based on the diagram,

(a). To determine the distance

We will apply the distance formula

$AD=AB+BD$

Insert the values into the equation

$D= 4+4.0\cos40^{\circ}$

$D=7.06\ km$

The resultant distance is 7.06 km westward.

(b). We will find the total displacement's magnitude

Using the displacement formula

$AC=\sqrt{(CD)^2+(AD)^2}$

Insert the values into the equation

$AC=\sqrt{(4.0\sin40)^2+(7.06)^2}$

$AC=7.51$

The total displacement magnitude is 7.51 km.

In conclusion, (a). The traveled distance is 7.06 km towards the west.

(b). The magnitude of their total displacement is 7.51 km.

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