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2 years ago

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A body goes from P to Q with a velocity of 10 m/s and comes back from Q to P with a velocity of 20 m/s. What is the average velo

city of the body during the entire trip?

1 answer:

Pachacha [2.7K]2 years ago

5 0

Let's say the distance is D. Then the time going is D/10 sec. The time returning is D/20 s. The total time is 3D/20 s, and the total distance is 2D. The average speed for the round trip is (total distance)/(total time). That's (2D) ÷ (3D/20). That's (40D/3D) which is 13-1/3 m/s. (I thought it was going to depend on the distance, but it doesn't.)

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what is the dot product and cross product of of two vectors if the angle is between them is 90 degree?

DaniilM [7]

$\sf{\pink{\underline{\underline{\blue{GIVEN:-}}}}}$

The angle between the two vectors is 90° .

$\sf{\pink{\underline{\underline{\blue{TO\: FIND:-}}}}}$

The dot product of two vectors .
The cross product of two vectors .

$\sf{\pink{\underline{\underline{\blue{SOLUTION:-}}}}}$

⚡ Let $\rm{\vec{a}}$ and $\rm{\vec{b}}$ are the two vectors .

✍️ We have know that,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:.\:\vec{b}\:=\:ab\cos{\theta}\:}}}}$

Where,

θ = 90°

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\cos{90^{\degree}}\:}$

cos 90° = <u>0</u>

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\times{0}\:}$

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:0\:}$

$\rm{\red{\therefore}}$ [1] The dot product of two vectors is “ <u>0</u> ” .

✍️ We have know that,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:\times\:\vec{b}\:=\:ab\sin{\theta}\:}}}}$

Where,

θ = 90°

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\sin{90^{\degree}}\:}$

sin 90° = <u>1</u>

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\times{1}\:}$

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\:}$

$\rm{\red{\therefore}}$ [2] The cross product of two vectors is “ <u>ab</u> ” .

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A resonant circuit using a 286-nFnF capacitor is to resonate at 18.0 kHzkHz. The air-core inductor is to be a solenoid with clos

lukranit [14]

Answer:

The inductor contains $N = 523962.32$ loops

Explanation:

From the question we are told that

The capacitance of the capacitor is $C = 286nF = 286 * 10^{-9} \ F$

The resonance frequency is $f = 18.0 kHz = 18*10^{3} Hz$

The diameter is $d = 1.1 mm = \frac{1.1 }{1000} = 0.00011 \ m$

The of the air-core inductor is $l = 12 \ m$

The permeability of free space is $\mu_o = 4 \pi *10^{-7} \ T \cdot m/A$

Generally the inductance of this air-core inductor is mathematically represented as

$L = \frac{\mu_o * N^2 \pi d^2}{4 l}$

This inductance can also be mathematically represented as

$L = \frac{1}{w^2}$

Where $w$ is the angular speed mathematically given as

$w = 2 \pi f$

So

$L = \frac{1}{4 \pi ^2 f^2}$

Now equating the both formulas for inductance

$\frac{\mu_o * N^2 \pi d^2}{4 l} = \frac{1}{4 \pi ^2 f^2}$

making N the subject of the formula

$N = \sqrt{\frac{1}{(2 \pi f)^2} * \frac{4 * l }{\mu_o * \pi d^2 C} }$

$N = \frac{1}{2 \pi f} * \frac{2}{d} * \sqrt{\frac{l}{\pi * \mu_o * C} }$

Substituting value

$N = \frac{1}{ 3.142 * 18*10^{3} * 0.00011 } \sqrt{\frac{12}{ 3.142 * 4 \pi *10^{-7}* 286 *10^{-9}} }$

$N = 523962.32$ loops

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What is air temperature meausered with?

vodka [1.7K]

Temperature is usually expressed in degrees Fahrenheit or Celsius. 0 degrees Celsius is equal to 32 degrees Fahrenheit. Room temperature is typically considered 25 degrees Celsius, which is equal to 77 degrees Fahrenheit.

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