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
nordsb [41]
3 years ago
6

Vector C has a magnitude of 24.6 m and points in the − y ‑ direction. Vectors A and B both have positive y ‑ components, and mak

e angles of α = 44.9 ° and β = 27.7 ° with the positive and negative x - axis, respectively. If the vector sum A + B + C = 0 , what are the magnitudes of A and B ?
Physics
1 answer:
frez [133]3 years ago
5 0

Answer:

A= 61.35

B= -44.40

Explanation:

1. Using the components method we have:

A_{x}= A cos \alpha\\B_{x}= B cos \beta\\C_{x}= 0\\\\A_{y}= A sin \alpha\\B_{y}= B sin \beta\\C_{y}= 24.6\\

Considering that the vector sum A+B+C=0, then:

|V|=\sqrt{V_{x}^{2} +V_{y}^{2} }=0

Then:

V_{x} ^{2} =0; V_{x} =0\\V_{y} ^{2} =0; V_{y} =0

It means the value of x and y component is 0.

2. Determinate the equations that describe each component:

V_{x}= A cos \alpha -B cos \beta=0  (1)\\V_{y}= A sin \alpha +B sin \beta - C=0   (2)

Form Eq. (1):

A=B \frac{cos \beta}{cos \alpha}     (3)

Replacing A in Eq. (2):

(B\frac{cos \beta}{cos \alpha})(sin \alpha)+ B sin\beta-C=0\\(B\frac{cos \beta}{cos \alpha})(sin \alpha)+ B sin\beta-=C\\\\B(\frac{cos \beta. sin \alpha}{cos \alpha}+ sin\beta)=C\\B=C(\frac{cos \beta. sin \alpha}{cos \alpha}+ sin\beta)^{-1}     (4)

Replacing values of C, α and β in (4):

B= 24.6 (\frac{(cos 27.7)(sin 44.9)}{cos 44.9}+sin 27.7)^{-1}  \\B= -44.4

Replacing value of B in (3)

A=-44.40\frac{cos 27.7}{sin 49.9} \\A= 61.35

You might be interested in
GUESS WHAT? I'LL MAKE YOU BRAINLIEST! EASY QUESTION!!
avanturin [10]

Here are the 2 reasons:

- Sun damages the eyes

Long-term, unprotected exposure to ultraviolet light from the sun can damage the retina. The retina is the back of the eye, where the rods and cones make visual images, which are then sent to the visual centers in the brain. Damage from exposure to sunlight can also cause the development of cloudy bumps along the edge of the cornea, which can then grow over the cornea and prevent clear vision. UV light is also a factor in the development of cataracts.

- Heat Exhaustion

According to the Centers for Disease Control and Prevention (CDC), heat exhaustion is the body’s response to excessive loss of water and salt, usually through excessive sweating. People working in a hot environment are at risk of heat exhaustion.

6 0
3 years ago
Read 2 more answers
Neither _____ nor _____ can be created or destroyed, but they can be changed from one to the other
Viktor [21]

Matter nor energy

hope this helps

3 0
3 years ago
Read 2 more answers
Steam types of<br> forces in<br> nature
max2010maxim [7]

Answer:

Gravity, Weak, Electromagnetic and Strong.

7 0
3 years ago
If an element's atomic mass and atomic number are known, what else can be determined? Give an example to demonstrate your unders
Alenkinab [10]

Answer:

Explanation:

If an elements atomic mass and number are known you can also determine the number of protons and neutrons it has. You can also determine where it is on the periodic table. For example, if a element had a atomic mass of 10 then it would be higher up on the table then one with a mass of 20. Btw I do apex too.

8 0
3 years ago
Read 2 more answers
An infinite line of charge with linear density λ1 = 6 μC/m is positioned along the axis of a thick insulating shell of inner rad
Anna11 [10]

Answer: λ2= 2.34 * 10^-6 C/m

Explanation: In order to calculate the value of the  linear charge density of the insulating shell we have to multiply ρ* Volume of the hollow cylinder, so

Volume of cylinder:2*π*b*L *(b-a)  where (b-a) is the thickness, then

λ2=Q/L = 634 *10^-6 C/m^3* 2*π*0.042 m*(0.042-0.26)== 2.34 μ C/m

5 0
3 years ago
Other questions:
  • Heat from burning fuel warms the walls of the firebox section of the furnace in
    8·1 answer
  • The unit light-year is a measure of
    9·2 answers
  • Sam is walking through the park. He hears a police car coming down the street toward him. What happens to the sound of the siren
    13·2 answers
  • A uniformly charged ring of radius 10.0 cm has a total charge of 75.0 mC. Find the electric field on the axis of the ring at (a)
    13·1 answer
  • A 20.0-m-tall hollow aluminum flagpole is equivalent in strength to a solid cylinder 4.00 cm in diameter. A strong wind bends th
    6·1 answer
  • A carnival game consists of a two masses on a curved frictionless track, as pictured below. The player pushes the larger object
    10·1 answer
  • A test of the prototype of a new automobile shows that the minimum distance for a controlled stop from 95 km/h to zero is 55 m.
    10·1 answer
  • How much power is needed to lift the 200-N object to a height of 4 m in 4 s?
    11·1 answer
  • Do you think antiseptic creams and lotions play an important part in our day<br>to day life? ​
    7·2 answers
  • -4, 0, -2/3, 4.11111…, 2, π, √6 'which members of this set are irrartional?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!