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A car travels 13 km in a southeast direction and then 16 km 40 degrees north of east. What is the car's resultant direction?

Answers

Answer 1

Answer:

Answer:

21.48 km 2.92° north of east

Explanation:

To find the resultant direction, we need to calculate a sum of vectors.

The first vector has module = 13 and angle = 315° (south = 270° and east = 360°, so southeast = (360+270)/2 = 315°)

The second vector has module 16 and angle = 40°

Now we need to decompose both vectors in their horizontal and vertical component:

horizontal component of first vector: 13 * cos(315) = 9.1924

vertical component of first vector: 13 * sin(315) = -9.1924

horizontal component of second vector: 16 * cos(40) = 12.2567

vertical component of second vector: 16 * sin(40) = 10.2846

Now we need to sum the horizontal components and the vertical components:

horizontal component of resultant vector: 9.1924 + 12.2567 = 21.4491

vertical component of resultant vector: -9.1924 + 10.2846 = 1.0922

Going back to the polar form, we have:

$module = √(horizontal^2 + vertical^2)$

$module = √(460.0639 + 1.1929)$

$module = 21.4769$

$angle = arc\ tangent(vertical/horizontal)$

$angle = arc\ tangent(1.0922/21.4491)$

$angle = 2.915\°$

So the resultant direction is 21.48 km 2.92° north of east.

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Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. show answer No Attempt Approximately what is the force due to the Bernoulli effect on a roof having an area of 205 m2? Typical air density in Boulder is 1.14 kg/m3 , and the corresponding atmospheric pressure is 8.89 × 104 N/m2 . (Bernoulli’s principle assumes a laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

Answers

Answer:

The force exerted on the roof is $F =2.37*10^(5)N$

Explanation:

From the question we are told that

The speed of the wind is $v = 45.0 m/s$

The area of the roof is $A = 205 m^2$

The air density of Boulder is $\rho = 1.14 kg / m^3$

The atmospheric pressure is $P_(atm) = 8.89 * 10^(4) N/ m^2$

For a laminar flow the Bernoulli’s principle is mathematically represented as

$P_1 + (1)/(2) \rho v_a ^2 + \rho g h_a = P_2 + (1)/(2) \rho v_b ^2 + \rho h_b$

Where $v_1$ is the speed of air in the building

$v_b$ is the speed of air outside the building

$P_1 \ and \ P_2$ are the pressure of inside and outside the house

$h_a \ and \ h_b$ are the height above and below the roof

Now for $h_a = h_b$

The above equation becomes

$P_1 + (1)/(2) \rho v_a ^2 = P_2 + (1)/(2) \rho v_b ^2$

$P_1 - P_2 = (1)/(2) \rho (v_b^2 - v_a^2)$

Since pressure is mathematically represented as

$P = (F)/(A )$

The above equation can be written as

$F = (1)/(2) \rho ( v_b^2 - v_a ^2 ) A$

The initial velocity is 0

Substituting value

$F = (1)/(2) (1.14) [(45^2 - 0^2 ) ](205)$

$F =2.37*10^(5)N$

An object is constrained by a cord to move in a circular path of radius 1-m on a frictionless, horizontal surface. The cord will break if the tension exceeds 26.9-N. The maximum kinetic energy that this object can have is _____ J. Round your answer to the nearest whole number.

Answers

Answer:

Explanation:

Let m be the mass of the object and v be the maximum velocity . The tension will provide centripetal force for the circular motion .

T = mv² / R where R is radius of circular path . T is tension .

putting the values given in the equation above

26.9 = m v² / 1

m v² = 26.9

kinetic enrgy = 1/2 m v²

= 26.9 / 2

= 13.45 J

13 J .

Maximum kinetic energy = 13 J .

Answer all three parts and show work.

Answers

The distance for both Parts A and B are given in the question.

A balloon drifts 140m toward the west in 45s.

The wind suddenly changes and the balloon flies 90m toward the east in the next 25s.

To find the total distance, we can just add.

140 + 90 = 230m

Best of Luck!

Two point charges have a total electric potential energy of -24 J, and are separated by 29 cm.If the total charge of the two charges is 45 μC, what is the charge, in μC, on the positive one?
What is the charge, in μC, on the negative one?

Answers

Answer:

The charge of the negative one is 13.27 microcoulombs and the positive one has a charge of 58.27 microcoulombs.

Explanation:

Electric potential energy between two point charges is derived from concept of Work, Work-Energy Theorem and Coulomb's Law and described by the following formula:

$U_(e) = (k\cdot q_(A)\cdot q_(B))/(r)$ (1)

Where:

$U_(e)$ - Electric potential energy, measured in joules.

$q_(A)$ , $q_(B)$ - Electric charges, measured in coulombs.

$r$ - Distance between charges, measured in meters.

$k$ - Coulomb's constant, measured in kilogram-cubic meters per square second-square coulomb.

If we know that $U_(e) = -24\,J$ , $q_(A) = 45* 10^(-6)\,C+ q_(B)$ , $k = 9* 10^(9)\,(kg\cdot m^(3))/(s^(2)\cdot C^(2))$ and $r = 0.29\,m$ , then the electric charge is:

$-24\,J = -(\left(9* 10^(9)\,(kg\cdot m^(3))/(s^(2)\cdot C^(2)) \right)\cdot (45* 10^(-6)\,C+q_(B))\cdot q_(B))/(0.29\,m)$

$-6.96 = -405000\cdot q_(B)-9* 10^(9)\cdot q_(B)^(2)$

$9* 10^(9)\cdot q_(B)^(2)+405000\cdot q_(B) -6.96 = 0$ (2)

Roots of the polynomial are found by Quadratic Formula:

$q_(B,1) = 1.327* 10^(-5)\,C$ , $q_(B,2) \approx -5.827* 10^(-5)\,C$

Only the first roots offer a solution that is physically reasonable. The charge of the negative one is 13.27 microcoulombs and the positive one has a charge of 58.27 microcoulombs.

An effect analogous to two-slit interference can occur with sound waves, instead of light. In an open field, two speakers placed 1.30 m apart are powered by a single function generator producing sine waves at 1200-Hz frequency. A student walks along a line 12.5 m away and parallel to the line between the speakers. She hears an alternating pattern of loud and quiet, due to constructive and destructive interference. What is : (a) the wavelength of this sound and (b) the distance between the central maximum and the first maximum (loud) position along this line

Answers

Answer:

2.72 m

Explanation:

wavelength of sound λ = velocity / frequency

= 340 / 1200

= .2833 m

Distance of point of first constructive interference

= λ D / d ( D is distance of the screen and d is distance between source of sound.

Here D = 12.5 m

d = 1.3 m

λ D / d= ( .2833 x 12.5) / 1.3

= 2.72 m

Distance of point of first constructive interference = 2.72 m

Final answer:

The wavelength of the produced sound is approximately 0.29 m. Constructive interference occurs when the path difference between the two waves is a multiple of this wavelength, allowing you to calculate the distance between the central maximum and first maximum loud position.

Explanation:

For part (a) of the question, we need to calculate the wavelength of the sound wave. The wave speed (v) is given by the multiplication of frequency (f) and wavelength (λ). The speed of sound in air is approximately 343 m/s and given that the frequency produced by the function generator is 1200 Hz, the wavelength can be calculated using the formula λ = v / f = 343 / 1200 ≈ 0.29 m.

For part (b) the distance between the central maximum (loud) position and the first maximum along this line requires understanding of sound wave interference and constructive interference. For constructive interference to occur, the path difference between the two waves needs to be a multiple of the wavelength. Thus, in the first constructive interference position (first maximum loud position), the path difference equals one wavelength (0.29m). Since the student is walking 12.5 m away and parallel to the line between the speakers (which is the hypotenuse of a right triangle stakeout, with one side being 0.65m), we can use Pythagorean theorem to find out the distance.

Learn more about Sound Waves Interference here:

brainly.com/question/1287906

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If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?a. 4
b. 2/pi
c. 2
d. (2)^1/2