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AleksandrR [38]

3 years ago

12

An optical fiber is made of clear plastic (n = 1.50). Light travels through the fiber at angles ranging from 40° to 55°. What is

the measurement of the critical angle of this fiber?

1 answer:

Arada [10]3 years ago

6 0

1/sinc = 1.50
sinc =1/1.5
critical angle = sininverse(1/1.5) = 41.8

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A water trough is m long and a cross-section has the shape of an isosceles trapezoid that is cm wide at the bottom, cm wide at t

Aleonysh [2.5K]

The rate of water level rising when the water is 30 cm deep will be 1/30 m/min.

<h3 /><h3>What is volume?</h3>

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

The complete question is;

"A water trough is 10m long and has a cross-section which is the shape of an isosceles trapezoid

that is 30cm wide at the bottom, 80cm wide at the top, and has a height of 50cm. If the trough is being filled with water at the rate of 0.2 m3/min, how fast is the water level rising when the water is 30cm deep?"

b1 is the width of the water at a height at the bottom

b2 is the width of the water at the height at the top

The length of the trapezoid is L

The volume of the trapezoid is found as;

$\rm V = 0.5(b_1 + b_2)hL$

The breadth rises by 1 as the height does, therefore which implies

$\rm \frac{dh}{dt} =\frac{dw}{dt}$

The water's breadth at the combined height is [0.3 + h]

$\rm V = 5h(0.3 +(0.3 + h))\\\\ V = 3h + 5h^2$

After differentiation we get;

$\rm \frac{dv }{dt} =3 \frac{dh}{dt} +10 h \frac{dh}{dt} \\\\\ \frac{ \frac{dv }{dt}}{3+10h}=\frac{dh}{dt} \\\\\ \frac{dv }{dt}= 0.2 \\\\\ h = 0.3 \\\\ \frac{dh}{dt} = \frac{1}{30} m/min$

Hence the rate of water level rising when the water is 30 cm deep will be 1/30 m/min.

To learn more about the volume, refer to brainly.com/question/1578538.

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6 0

2 years ago

A Force is applied onto a mass causing it to accelerate. If the same Force was applied to a SMALLER mass, what would happen to t

konstantin123 [22]

Answer:

1. The acceleration would increase.

Explanation:

This is because according to Newton's law, the less mass there is, the more velocity.

3 0

3 years ago

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A hawk flying at 11 m/s at an altitude of 132 m accidentally drops its prey. The parabolic trajectory of the falling prey is des

WITCHER [35]

Answer:

s = 153.34 m

Explanation:

given,

speed of hawk flying = 11 m/s

altitude = 132 m

equation of parabolic trajectory

$y = 132 -\dfrac{x^2}{33}$ ............at y = 0 x =66

$ds=\sqrt{dx^2+dy^2}$

$ds=dx\sqrt{1+(\dfrac{dy}{dx})^2}$

$\dfrac{dy}{dx}=\dfrac{-2x}{33}$

$ds=dx\sqrt{1+(\dfrac{-2x}{33} )^2}$

$ds=dx\sqrt{1+(\dfrac{4x^2}{1089} )}$

integrating

$s = \int _0^66\sqrt{1+(\dfrac{4x^2}{1089} )}$

using formula

$\sqrt{x^2+a^2}=\dfrac{x}{2}\sqrt{x^2+a^2}+\dfrac{a^2}{2}log|x+\sqrt{x^2+a^2}|$

s = 153.34 m

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3 years ago

A 1.25 m long pendulum on Mars

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Try to repost so somebody answer

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3 years ago

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At what speed, as a fraction of c , is a particle's total energy twice its rest energy

WINSTONCH [101]

The rest energy of a particle is
$E_0=m_0 c^2$
where $m_0$ is the rest mass of the particle and c is the speed of light.

The total energy of a relativistic particle is
$E=mc^2 = \frac{m_0 c^2}{ \sqrt{1- \frac{v^2}{c^2} } }$
where v is the speed of the particle.

We want the total energy of the particle to be twice its rest energy, so that
$E=2E_0$
which means:
$\frac{m_0c^2}{ \sqrt{1- \frac{v^2}{c^2} } }=2m_0 c^2$
$\frac{1}{ \sqrt{1- \frac{v^2}{c^2} } }=2$
From which we find the ratio between the speed of the particle v and the speed of light c:
$\frac{v}{c}= \sqrt{1- (\frac{1}{2})^2 } =0.87$
So, the particle should travel at 0.87c in order to have its total energy equal to twice its rest energy.

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3 years ago