Select the correct answer.

A 2.93 kg particle has a velocity of (2.98 i hat - 3.98 j) m/s.

cupoosta [38]

Answer:

a) The x and y components of the momentum are $8.731\,\frac{kg\cdot m}{s}$ and $-11.661\,\frac{kg\cdot m}{s}$ , respectively.

b) The magnitude and direction of its momentum are approximately 14.567 kilogram-meters per second and 306.823º.

Explanation:

a) The vectorial equation of momentum is represented by the following expression:

$\vec p = m\cdot \vec v$ (1)

Where:

$\vec p$ - Vector momentum, measured in kilogram-meters per second.

$m$ - Mass of the particle, measured in kilograms.

$\vec v$ - Vector velocity, measured in meters per second.

If we know that $m = 2.93\,kg$ and $\vec v = 2.98\,\hat{i}-3.98\,\hat{j}\,\,\,\left[\frac{m}{s} \right]$ , then the momentum is:

$\vec p = (2.93)\cdot (2.98\,\hat{i}-3.98\,\hat{j})\,\,\,\left[\frac{kg\cdot m}{s} \right]$

$\vec p = 8.731\,\hat{i}-11.661\,\hat{j}\,\,\,\left[\frac{kg\cdot m}{s} \right]$

The x and y components of the momentum are $8.731\,\frac{kg\cdot m}{s}$ and $-11.661\,\frac{kg\cdot m}{s}$ , respectively.

b) The magnitude and direction of momentum are represented by the following expressions:

$\|\vec p \| = \sqrt{p_{x}^{2}+p_{y}^{2}}$ (2)

$\theta = \tan^{-1}\left(\frac{p_{y}}{p_{x}} \right)$ (3)

Where:

$\|\vec p\|$ - Magnitude of momentum, measured in kilogram-meters per second.

$\theta$ - Direction of momentum, measured in sexagesimal degrees.

If we know that $p_{x} = 8.731\,\frac{kg\cdot m}{s}$ and $p_{y} = -11.661\,\frac{kg\cdot m}{s}$ , then the magnitude and direction of momentum are, respectively:

$\|\vec p\| = \sqrt{\left(8.731\,\frac{kg\cdot m}{s} \right)^{2}+\left(-11.661\,\frac{kg\cdot m}{s} \right)^{2}}$

$\|\vec p\| \approx 14.567\,\frac{kg\cdot m}{s}$

$\theta =\tan^{-1}\left(\frac{-11.661\,\frac{kg\cdot m}{s} }{8.731\,\frac{kg\cdot m}{s} } \right)$

$\theta \approx 306.823^{\circ}$

The magnitude and direction of its momentum are approximately 14.567 kilogram-meters per second and 306.823º.

6 0

3 years ago

A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 43.0 vibrations

blsea [12.9K]

Answer:

0.218

Explanation:

Given that

Total vibrations completed by the wave is 43 vibrations

Time taken to complete the vibrations is 33 seconds

Length of the wave is 424 cm = 4.24 m

to solve this problem, we first find the frequency.

Frequency, F = 43 / 33 hz

Frequency, F = 1.3 hz

Also, we find the wave velocity. Which is gotten using the relation,

Wave velocity = 4.24 / 15

Wave velocity = 0.283 m/s

Now, to get our answer, we use the formula.

Frequency * Wavelength = Wave Velocity

Wavelength = Wave Velocity / Frequency

Wavelength = 0.283 / 1.3

Wavelength = 0.218

7 0

2 years ago

A planetâs moon revolves around the planet with a period of 39 Earth days in an approximately circular orbit of radius of 4.8Ã10

Alchen [17]

Answer:

v = 895 m/s

Explanation:

Time period is given as 39 Earth Days

$T = 39 days \times 24 hr \times 3600 s$

$T = 3369600 s$

now the radius of the orbit is given as

$r = 4.8 \times 10^8 m$

so the total path length is given as

$L = 2 \pi r$

$L = 2\pi (4.8 \times 10^8)$

$L = 3.015 \times 10^9$

now the speed will be given as

$v = \frac{L}{T}$

$v = \frac{3.015 \times 10^9}{3369600}$

$v = 895 m/s$

7 0

3 years ago

A 3000-N force gives an object an acceleration of 15 m/s2. The mass of the object is

7nadin3 [17]

<h3>Answer:</h3>

200 kg

<h3>General Formulas and Concepts:</h3>

Math

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Physics

Newton's Law of Motions

Newton's 1st Law of Motion: An object at rest remains at rest and an object in motion stays in motion

Newton's 2nd Law of Motion: F = ma (Force is equal to [constant] mass times acceleration)

Newton's 3rd Law of Motion: For every action, there is an equal and opposite reaction

<h3>Explanation:</h3>

Step 1: Define

[Given] F = 3000 N

[Given] a = 15 m/s²

[Solve] m = x kg

Step 2: Solve for m

Substitute in variables [Newton's Second Law of Motion]: 3000 N = m(15 m/s²)
[Mass] [Division Property of Equality] Isolate m [Cancel out units]: 200 kg = m
[Mass] Rewrite: m = 200 kg

5 0

2 years ago

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marusya05 [52]

Earthquakes happen when rock below the Earth's surface moves abruptly. Usually, the rock is moving along large cracks in Earth's crust called faults. Most earthquakes happen at or near the boundaries between Earth's tectonic plates because that's where there is usually a large concentration of faults

7 0

3 years ago

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