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3 years ago

12

Two converging lenses, one with f = 4.0 cm and the other with f = 37 cm , are made into a telescope. What is the length of this

telescope?
What is the magnification of this telescope?

1 answer:

d1i1m1o1n [39]3 years ago

8 0

Answer:

The length and the magnification of this telescope are 41 cm and 0.108.

Explanation:

Given that,

Focal length of first lens f= 4.0 cm

Focal length of other lens f'= 37 cm

We need to calculate the length of the telescope

Using formula of length

$L=f+f'$

Put the value into the formula

$L=4+37=41 cm$

We need to calculate the magnification of the telescope

Using formula of the magnification

$m=\dfrac{f}{f'}$

Put the value into the formula

$m=\dfrac{4}{37}$

$m=0.108$

Hence, The length and the magnification of this telescope are 41 cm and 0.108.

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Explanation:

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2 years ago

After flying for 15 min in a wind blowing 42 km/h at an angle of 19° south of east, an airplane pilot is over a town that is 48

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Answer:

The speed of the airplane relative to the air is 209.47km/hr

Explanation:

Whenever we are solving a physics problem, it's really useful to start by drawing a diagram of the problem (See picture attached). It will help us visualize the problem better.

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$15min*\frac{1hr}{60min}=0.25hr$

Once our time is rewritten as hours, we can now calculate the velocity towards north of the plane.

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$V=\frac{48km}{0.25hr}$

so

V=192km/hr j

Now, we can calculate the x and y-components of the velocity of the wind. The problem states that the wind is blowing at 42km/hr at an angle of 19° south of east, so the x and y-components of the velocity of the wind are:

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and

$V_{y}=42km/hr*sin(-19^{o} )=-13.67 j$

So the velocity of the wind can be expressed as a vector as:

$V_{wind}=(39.71i - 13.67j)km/hr$

Once we know this, we can find the velocity of the plane with respect of the wind on x and on y:

$V_{plane x}=V_{plane/wind x}+V_{wind x}$

$V_{plane/wind x}=V_{plane x}-V_{wind x}$

$V_{plane/wind x}=(0-39.71 i)km/hr$

$V_{plane/wind x}= -39.71 i km/hr$

and

$V_{plane y}=V_{plane/wind y}+V_{wind y}$

$V_{plane/wind y}=V_{plane y}-V_{wind y}$

$V_{plane/wind y}=192km/hr j - (- 13.67j)km/hr$

$V_{plane/wind x}= 205.67 j km/hr$

So the velocity of the plane with respect to the wind can be rewritten as:

$V_{plane/wind x}= (-39.71i + 205.67 j) km/hr$

Since the problem asks us to find the speed of the plane with respect to the wind, this means that we need to find the magnitude of the velocity, since the speed is a scalar defined to be the magnitude of the velocity.

so:

$speed=\sqrt{(-39.71)^{2}+(205.67)^{2} }$

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