Ask question

Ask question

All categories

3 years ago

7

An 7.5 × binocular has 3.7-cm-focal-length eyepieces. What is the focal length of the objective lenses? Express your answer to t

wo significant figures and include the appropriate units.

1 answer:

elixir [45]3 years ago

5 0

To solve this problem we will apply the concept of magnification, which is given as the relationship between the focal length of the eyepieces and the focal length of the objective. This relationship can be expressed mathematically as,

$\mu = \frac{f_0}{f_e}$

Here,

$\mu$ = Magnification

$f_e$ = Focal length eyepieces

$f_0$ = Focal length of the Objective

Rearranging to find the focal length of the objective

$f_0 = \mu f_e$

Replacing with our values

$f_0 = 7.5* 3.7cm$

$f_0 = 27.75cm$

Therefore the focal length of th eobjective lenses is 27.75cm

You might be interested in

Dose aloe Vera grow in the mesa?

Zina [86]

there are diffrent species of aloe vera so there is

3 0

3 years ago

A vertical spring withk= 245N/m oscillates with an amplitude of 19.2cm when 0.457kg hangs from it. The mass posses through the e

Makovka662 [10]

Answer:

y = -19.2 sin (23.15t) cm

Explanation:

The spring mass system is an oscillatory movement that is described by the equation

y = yo cos (wt + φ)

Let's look for the terms of this equation the amplitude I

y₀ = 19.2 cm

Angular velocity is

w = √ (k / m)

w = √ (245 / 0.457

w = 23.15 rad / s

The φ phase is determined for the initial condition t = 0 s , the velocity is negative v (0) = -vo

The speed of the equation is obtained by the derivative with respect to time

v = dy / dt

v = - y₀ w sin (wt + φ)

For t = 0

-vo = -yo w sin φ

The angular and linear velocity are related v = w r

v₀ = w r₀

v₀ = v₀ sinφ

sinφ = 1

φ = sin⁻¹ 1

φ = π / 4 rad

Let's build the equation

y = 19.2 cos (23.15 t + π/ 4)

Let's use the trigonometric ratio π/ 4 = 90º

Cos (a +90) = cos a cos90 - sin a sin sin 90 = 0 - sin a

y = -19.2 sin (23.15t) cm

8 0

3 years ago

Daring Darless wishes to cross the Grand Canyon of the Snake River by being shot from a cannon. She wishes to be launched at 65

guajiro [1.7K]

Answer:

She must be launched with minimum speed of <u>57.67 m/s</u> to clear the 520 m gap.

Step-by-step explanation:

Given:

The angle of projection of the projectile is, $\theta =65$ °

Range of the projectile is, $R=520$ m.

Acceleration due to gravity, $g=9.8\ m/s^2$

The minimum speed to cross the gap is the initial speed of the projectile and can be determined using the formula for range of projectile.

The range of projectile is given as:

$R=\frac{v_{0}^2\sin2\theta}{g}$

Plug in all the given values and solve for minimum speed, $v_0$ .

$520=\frac{v_{0}^2\sin(2(65))}{9.8}\\520\times 9.8=v_{0}^2\sin(130)\\5096=1.532v_{0}^2\\v_0^2=\frac{5096}{1.532}\\v_0^2=3326.371\\v_0=\sqrt{3326.371}=57.67\textrm{ m/s}$

Therefore, she must be launched with minimum speed of 57.67 m/s to clear the 520 m gap.

3 0

3 years ago

A 2.0 m conductor is formed into a square and placed in the horizontal xy-plane. A magnetic field is oriented 30.0° above the ho

Gnesinka [82]

Answer:

$\phi_B = 0.216 T m^2$

Explanation:

As we know that the length of the conductor is given as

$L = 2 m$

now if it is converted into a square then we have

$L = 4a$

$a = \frac{L}{4} = 0.5 m$

now the are of the loop will be

$A = a^2 = 0.5(0.5) = 0.25 m^2$

now the magnetic flux is defined as

$\phi_B = BAcos\theta$

here we know

B = 1.0 T

$\theta = 30.0^o$

$\phi_B = (1.0 T)(0.25 m^2)(cos30)$

$\phi_B = 0.216 T m^2$

5 0

3 years ago

What factors could enhance memory and kept constant? and why

artcher [175]

To help make sure information goes from short-term memory to long-term memory, you can use memory-enhancing strategies. One strategy is rehearsal, or the conscious repetition of information to be remembered. Think about how you learned your multiplication tables as a child.

Proven ways to protect memory include following a healthy diet, exercising regularly, not smoking, and keeping blood pressure, cholesterol, and blood sugar in check. Living a mentally active life is important, too. Just as muscles grow stronger with use, mental exercise helps keep mental skills and memory in tone.

According to one study, mental stimulation like reading can help protect memory and thinking skills, especially as you age. The authors even suggest that reading every day can slow down the late-life cognitive decline. ... The act of reading helps to heighten overall brain function and increase memory.

Let's take a deeper dive into evidence-based exercises that offer the best brain-boosting benefits.

Have fun with a jigsaw puzzle. ...

Try your hand at cards. ...

Build your vocabulary. ...

Dance your heart out. ...

Use all your senses. ...

Learn a new skill. ...

Teach a new skill to someone else. ...

Listen to or play music.

8 0

2 years ago