1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MissTica
2 years ago
12

The two vectors and in fig. 3-28 have equal magnitudes of 10.0 m and the angles are 30° and 105°. find the (a) x and (b) y compo

nents of their vector sum , (c) the magnitude of , and (d) the angle makes with the positive direction of the x axis.
Physics
1 answer:
mylen [45]2 years ago
6 0

You can just use basic trigonometry to solve for the x & y components.

<span>vector a = 10cos(30) i + 10sin(30) j = <5sqrt(3), 5></span>

vector b is only slightly harder because the angle is relative to vector a, and not the positive x-axis. Anyway, this just makes vector b with an angle of 135deg to the positive x-axis.

<span>vector b = 10cos(135) i + 10sin(135) j = <-5sqrt(2), 5sqrt(2)></span>

So now we can do the questions:

r = a + b

r = <5sqrt(3)-5sqrt(2), 5+5sqrt(2)>

(a) 5sqrt(3)-5sqrt(2)

(b) 5+5sqrt(2)

(c)

|r| = sqrt( (5sqrt(3)-5sqrt(2))2 + (5+5sqrt(2))2 )

= 12.175

(d)

θ = tan-1 ( (5+5sqrt(2)) / (5sqrt(3)-5sqrt(2)) )

θ = 82.5deg

<span> </span>

You might be interested in
The pupil of the human eye can vary in diameter from 2.00 mm in bright light to 8.00 mm in dim light. The eye has a focal length
Zarrin [17]

The indicated data are of clear understanding for the development of Airy's theory. In optics this phenomenon is described as an optical phenomenon in which The Light, due to its undulatory nature, tends to diffract when it passes through a circular opening.

The formula used for the radius of the Airy disk is given by,

y_r=1.22\frac{\lambda f}{d}

Where,

y_r = Range of the radius

\lambda = wavelength

f= focal length

Our values are given by,

State 1:

d=2.00mm = 2*10^{-3}m

f= 25mm = 25*10^{-3}m

\lambda = 750nm = 750*10^{-9}m

State 2:

d=8.00mm = 8*10^{-3}m

f= 25mm = 25*10^{-3}m

\lambda = 390nm = 390*10^{-9}

Replacing in the first equation we have:

y_{r1} = 1.22\frac{(750*10^{-9})(25*10^{-3})}{2*10^{-3}}

y_{r1}= 11.4\mu m

And also for,

y_{r2} =1.22\frac{(390*10^{-9})(25*10^{-3})}{8*10^{-3}}

y_{r2} = 1.49\mu m

Therefor, the airy disk radius ranges from 1.49\mu m to 11.4\mu m

7 0
3 years ago
Explain how you think humans have disrupted the nitrogen cycle HELP QUICK DUE APRIL 15TH ANYBODY
mina [271]

Answer:

Scientists have determined that humans are disrupting the nitrogen cycle by altering the amount of nitrogen that is stored in the biosphere. The chief culprit is fossil fuel combustion, which releases nitric oxides into the air that combine with other elements to form smog and acid rain.

5 0
2 years ago
If an otherwise empty pressure cooker is filled with air of room temperature and then placed on a hot stove, what would be the m
Xelga [282]

Answer:

The magnitude of the net force F₁₂₀ on the lid when the air inside the cooker has been heated to 120 °C is \frac{135.9}{A}N

Explanation:

Here we have

Initial temperature of air T₁ = 20 °C = ‪293.15 K

Final temperature of air T₁ = 120 °C = 393.15 K

Initial pressure P₁ = 1 atm = ‪101325 Pa

Final pressure P₂ = Required

Area = A

Therefore we have for the pressure cooker, the volume is constant that is does not change

By Chales law

P₁/T₁ = P₂/T₂

P₂ = T₂×P₁/T₁ = 393.15 K× (‪101325 Pa/‪293.15 K) = ‭135,889.22 Pa

∴ P₂ = 135.88922 KPa = 135.9 kPa

Where Force = \frac{Pressure}{Area} we have

Force = F_{120}=\frac{135.9}{A}N.

4 0
3 years ago
A certain pendulum with a 1.00 kg bob has a period of 3.50 s. What will happen to the period of the pendulum if the 1.00 kg bob
Serggg [28]

Answer:

The period will be doublef because increasing the mass increases the period linearly.

Explanation:

A stiffer spring with a constant mass decreases the period of oscillation. Increasing the mass increases the period of oscillation

8 0
3 years ago
How can we alter the pitch of guitar
zhenek [66]

Answer:

Tuning the keys.

Explanation:

<em>"Guitar strings are tuned (tightened and loosened) using their tuning keys. </em><em>Applying too much tension to a string tightly can raise it to the pitch of the next note, while loosening it can easily lower it the same amount.</em><em> Increasing the tension raises the pitch. The length of a string is also important."</em>

<em />

I hope this answers your question! Have a good night!

4 0
2 years ago
Read 2 more answers
Other questions:
  • The average marathon is 42 km long. If the average person can run the marathon with an average velocity of 2.57 m/s, how long wi
    13·1 answer
  • What is the distance between two points (3,4,-5) and (2,1,0,)
    14·1 answer
  • Sam makes six star-shaped cookies out of dough. He puts all of the cookies on a balance and measures the total weight as 36 gram
    14·1 answer
  • Which type of place is rich in biodiversity?​
    13·1 answer
  • PLEASE HELP THIS IS A 53 QUESTION TEST
    13·1 answer
  • according to newton's first law of motion what is the reason for a ball throwing up in the airfall back to earth
    12·1 answer
  • - A certain mass is suspended at one end of a spring of spring-constant of 32,000gm/s2. The
    9·1 answer
  • How do gases respond to changes in pressure and temperature?
    7·2 answers
  • What is the fastest motion that can be measured in any frame of reference?
    14·1 answer
  • A 2.0 x 10^3-kilogram car travels at a constant speed of 12 meters per second around a circular curve of radius 30. meters. What
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!