Physics, 27.10.2020 23:00 jamalnellum56

You are given two vectors A⃗ =−3.00i^+7.00j^ and B⃗ =5.00i^+2.00j^. Let counterclockwise angles be positive. 1- What angle θA, where 0∘≤θA<360∘, does A⃗ make with the +x-axis?
2-What angle θB, where 0∘≤θB<360∘, does B⃗ make with the +x-axis?
Express your answer in degrees.
3-Vector C⃗ is the sum of A⃗ and B⃗ , so C⃗ =A⃗ +B⃗ . What angle θC, where 0∘≤θC<360∘, does C⃗ make with the +x-axis?
Express your answer in degrees

Answers: 2

Show answers

Answers

Answer from: jcazares3558

1) The solution is $\theta_{1} \approx 113.141^{\circ}$ .

2) The solution is $\theta_{1} \approx 21.874^{\circ}$ .

3) The solution is $\theta_{1} \approx 77.467^{\circ}$ .

1) In this case, we can determine the angle, measured in sexagesimal degrees, with respect to the x-axis by definition of dot point:

$\cos \theta = \frac{\vec A\,\bullet \, \vec u}{\|\vec A\|\cdot \|\vec u\|}$ (1)

Where $\|\vec A\|$ and $\|\vec u\|$ are the norms of $\vec A$ and $\vec u$ .

If we know that $\vec A = (-3, 7)$ and $\vec u = (1, 0)$ , then the angle that $\vec A$ make with the x-axis is:

$\|\vec A\| = \sqrt{(-3)^{2}+7^{2}}$

$\|\vec A\| = \sqrt{58}$

$\|\vec u\| = 1$

$\cos \theta = \frac{(-3)\cdot (1)}{\sqrt{58} \cdot 1}$

$\cos \theta \approx -0.393$

The solution is $\theta_{1} \approx 113.141^{\circ}$ .

2) In this case, we can determine the angle, measured in sexagesimal degrees, with respect to the x-axis by definition of dot point:

$\cos \theta = \frac{\vec B\,\bullet \, \vec u}{\|\vec B\|\cdot \|\vec u\|}$ (1)

Where $\|\vec B\|$ and $\|\vec u\|$ are the norms of $\vec B$ and $\vec u$ .

If we know that $\vec B = (5, 2)$ and $\vec u = (1, 0)$ , then the angle that $\vec A$ make with the x-axis is:

$\|\vec B\| = \sqrt{5^{2}+2^{2}}$

$\|\vec B\| = \sqrt{29}$

$\|\vec u\| = 1$

$\cos \theta = \frac{(5)\cdot (1)}{\sqrt{29} \cdot 1}$

$\cos \theta \approx 0.928$

The solution is $\theta_{1} \approx 21.874^{\circ}$ .

3) In this case, we need to find the value of $\vec C$ by vectorial sum before calculating the angles with respect to x-axis:

$\vec C = \vec A + \vec B = (-3, 7) + (5, 2)$

$\vec C = (2, 9)$

In this case, we can determine the angle, measured in sexagesimal degrees, with respect to the x-axis by definition of dot point:

$\cos \theta = \frac{\vec C\,\bullet \, \vec u}{\|\vec C\|\cdot \|\vec u\|}$ (1)

Where $\|\vec C\|$ and $\|\vec u\|$ are the norms of $\vec C$ and $\vec u$ .

If we know that $\vec B = (2, 9)$ and $\vec u = (1, 0)$ , then the angle that $\vec A$ make with the x-axis is:

$\|\vec C\| = \sqrt{2^{2}+9^{2}}$

$\|\vec C\| = \sqrt{85}$

$\|\vec u\| = 1$

$\cos \theta = \frac{(2)\cdot (1)}{\sqrt{85} \cdot 1}$

$\cos \theta \approx 0.217$

The solution is $\theta_{1} \approx 77.467^{\circ}$ .

We kindly invite you to see this question related to angles and dot product: link

Answer from: lay1649

Ax = -3 By= 7 tan phi = -7 / 3 phi = -66.8

Since theta is in the second quadrant theta = 180 - 66.8 = 113.2 deg

Bx = 5 By = 2 tan theta = .4 theta = 21.8 deg

Cx = Ax + Bx = 2 Cy = Ay + By = 9

tan theta = 9 / 2 = 4.5 theta = 77.5 deg

Answer from: Quest

This is what i found on google “according to the collision theory, the following criteria must be met in order for a chemical reaction to occur: molecules must collide with sufficient energy, known as the activation energy, so that chemical bonds can break. molecules must collide with the proper orientation.” i hope this information you.

Answer from: Quest

answer: you might love summer weather, but you don’t want it to feel like the sun is inside your car. but a hot car that just won’t seem to cool down might be a bigger of a problem than you think. your car relies on being at the right temperature.

explanation:

Another question on Physics

Physics, 22.06.2019 15:50

An object with initial temperature 130 ∘ f is submerged in large tank of water whose temperature is 50 ∘ f . find a formula for f ( t ) , the temperature of the object after t minutes, if the cooling constant is k = − 0.2 . remember newton's law of cooling (the rate of change of temperature with respect to time is equal to k times the difference between the temperature of the object and the surrounding temperature) ! : )

Answers: 1

Answer

Physics, 22.06.2019 16:30

He latent heat of vaporization for ethyl alcohol is 854 j/g. the amount of energy, rounded to the nearest whole number, needed to change 5.20 grams of ethyl alcohol from a liquid to a gas is

Answers: 2

Answer

Physics, 22.06.2019 17:00

In the future, people will only enjoy one sport: electrodisc. in this sport, you gain points when you cause metallic discs hovering on a field to exchange charge. you are an electrodisc player playing the popular four disc variant. the disks have charges of qa = −8.0 µc, qb = −2.0 µc, qc = +5.0 µc, and qd = +12.0 µc. (1) you bring two disks together and then separate them. you measure the resulting charge of these two disks and find that it is +5.0 µc per disk. which two disks did you bring together? (a) a and b (b) a and c (c)a and d (d)b and c(e) b and d (f) c and d. (2) you bring three disks together and then separate them. you measure the resulting charge of these three disks and find that it is +3.0 µc per disk. which three disks did you bring together? a, b, and c (a) a, b, and d (c) a, c, and d (d) b, c, and d. (3) given the resulting charge of each disk measured in (b) is +3.0 µc, how many electrons would you need to add to a disk of this charge to electrically neutralize it? electrons

Answers: 3

Answer

Physics, 22.06.2019 20:50

In a game of pool, ball a is moving with a velocity v0 of magnitude v0 = 15 ft/s when it strikes balls b and c, which are at rest and aligned as shown. knowing that after the collision the three balls move in the directions indicated and assuming frictionless surfaces and perfectly elastic impact (that is, conservation of energy), determine the magnitudes of the velocities va, vb, and vc.

Answers: 3

Answer

You know the right answer?

You are given two vectors A⃗ =−3.00i^+7.00j^ and B⃗ =5.00i^+2.00j^. Let counterclockwise angles be p...

Questions