A 1000 kg car and a 1500 kg car are driving in opposite directions at 20 m/s and 10 m/s respectively. If the cars collide head-on and stick together, determine their combined speed after the collision.

Let m₁ and v₁ denote the mass and initial velocity of the first ball, and m₂ and v₂ the same quantities for the second ball. Momentum is conserved throughout the collision, so

m₁ v₁ + m₂ v₂ = m₁ v₁' + m₂ v₂'

where v₁' and v₂' are the balls' respective velocities after the collision.

Kinetic energy is also conserved, so

1/2 m₁ v₁² + 1/2 m₂ v₂² = 1/2 m₁ (v₁')² + 1/2 m₂ (v₂')²

or

m₁ v₁² + m₂ v₂² = m₁ (v₁')² + m₂ (v₂')²

From the momentum equation, we have

(0.600 kg) (9.00 m/s) + (0.300 kg) (-8.00 m/s) = (0.600 kg) v₁' + (0.300 kg) v₂'

which simplifies to

10.0 m/s = 2 v₁' + v₂'

so that

v₂' = 10.0 m/s - 2 v₁'

From the energy equation, we have

(0.600 kg) (9.00 m/s)² + (0.300 kg) (-8.00 m/s)² = (0.600 kg) (v₁')² + (0.300 kg) (v₂')²

which simplifies to

67.8 J = (0.600 kg) (v₁')² + (0.300 kg) (v₂')²

or

226 m²/s² = 2 (v₁')² + (v₂')²

Substituting v₂' yields

226 m²/s² = 2 (v₁')² + (10.0 m/s - 2 v₁')²

which simplifies to

3 (v₁')² - (20.0 m/s) v₁' - 63.0 m²/s² = 0

Solving for v₁' using the quadratic formula gives two solutions,

v₁' ≈ -2.33 m/s   or   v₁' = 9.00 m/s

but the second solution corresponds to the initial conditions, so we omit that one.

Then the second ball has velocity

v₂' = 10.0 m/s - 2 (-2.33 m/s)

v₂' ≈ 14.7 m/s

3. Distance is a quantity that is always a vector.

B.

Explanation:

Joule is unit of work or energy in the International System of Units (SI)

[tex] \large \mathfrak {Formula}[/tex]

work (joules) = force (newtons) x distance (meters)

[tex] \large\mathfrak{Invented \: by} [/tex]

James Prescott Joule

Answer:

Give person above me brainliest

Explanation:

Answer:

E.visible lights

Explanation:

llll

hope its attachments

Answer:

Atom, the cross-platform, open source code editor developed by Github, has become quite popular thanks to its plug-ins and embedded Git Control. ... There are, however, official Atom repositories for some Linux distributions, like Ubuntu, Debian, Fedora, Red Hat, CentOS, and open.

Answer:

1176.798 J

Explanation:

[] Use the following equation:

U = mgh

m - mass

g - gravitational field

h - height

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

>400N is needed to balance that lever

Answer:

42 Joules

Explanation:

Potential energy

= weight × height

= (3.5)(12)

= 42 joules

Answer:

i think wave lengh not 100% sure tho

If the energy of the mechanical wave will increase or decrease, then the wavelength will also change accordingly. Hence, option A is correct.

The distance between two identical locations (adjacent crests) in successive cycles is known as the wavelength, and it is used to describe waveform signals that are transmitted over wires or into space. Typically, in wireless systems, this length is specified in meters (m), centimeters (cm), or millimeters (mm). The wavelength is more frequently described in nanometers (nm), which are units of 10⁻⁹ m, or angstroms, which are units of 10⁻¹⁰ m, for infrared (IR), visible light (UV), and gamma radiation.

Frequency, which is defined as the number of wave cycles per second, and wavelength have an inverse relationship. The wavelength of a signal decreases with increasing frequency, or we can say that wavelength and refractive index are inversely proportional to each other.

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Answer:

Explanation:

The concept of a new strong nuclear force was introduced. In 1935, the first theory for this new force was developed by the Japanese physicist Hideki Yukawa, who suggested that the nucleons would exchange particles between each other and this mechanism would create the force.

Answer:

all the ones that say

Explanation:

18.....

North Carolina is one of the states is the age of consent 18 years old. Hence option A is correct.

A state is a type of centralised political entity that establishes and upholds laws over a population within a given region. A state's definition is open to debate. Although alternative definitions are widespread, the German sociologist Max Weber's is the most generally used: a "state" is a polity that retains a monopoly on the legal use of violence. Statelessness societies like the Haudenosaunee Confederacy, which "do not have either purely or even primarily political institutions or roles," are examples of societies in which the lack of a state does not prohibit the existence of a community. A state's degree of governance, which is used to assess its success or failure, is thought of as the core component of modern states.

Hence option A is correct.

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Answer:

[tex]\huge\boxed{\sf S = 18.75 \ meters}[/tex]

Explanation:

Given Data:

Initial Velocity = Vi = 0 m/s (rest)

Final Velocity for 6 seconds = Vf = 25 m/s

Time (1) = T1 = 6 seconds

Time (2) = T2 = 3 seconds

Required:

Distance for 3 seconds = S = ?

Solution:

For 6 seconds, the acceleration will be:

[tex]\displaystyle a = \frac{Vf-Vi}{t} \\\\a = \frac{25 - 0}{6} \\\\a = 25 / 6\\\\\boxed{a = 4.167 \ m/s^2}[/tex]

Since, acceleration is constant, it will be the same at 3 seconds as well.

Using second equation of motion to find Distance (S) with time being 3 seconds:

[tex]\displaystyle S= Vit+\frac{1}{2} at^2\\\\S = (0)(3)+ \frac{1}{2} (4.167)(3)^2\\\\S = \frac{1}{2} (4.167)(9)\\\\S = \frac{37.5}{2} \\\\\boxed{S = 18.75 \ meters}\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

3000N

Explanation:

divided to get answer

the force needed to accelerate the 1000kg car by 3m/s2 is 3000N

The mass of the boulder is equal to 16.10 kilograms.

Given the following data:

To determine the mass of the boulder:

Mathematically, potential energy (P.E) is calculated by using the following formula:

[tex]P.E = mgh[/tex]

Where:

Making m the subject of formula, we have:

[tex]m = \frac{P.E}{gh}[/tex]

Substituting the given parameters into the formula, we have;

[tex]m=\frac{7100}{9.8 \times 45} \\\\m=\frac{7100}{441}[/tex]

Mass, m = 16.10 kg

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Answer:

depth from optical expansion

Explanation:

Answer:

The more mass an object has, the greater its gravitational field and gravity force will be.

Explanation:

gravity force = mass × gravitational field strength (g)

The more mass, the more g-force.

Answer:

Doubling the large mass

Explanation:

By doubling the mass you will get more gravational force

The velocity of the pitcher at the given mass is 0.1 m/s.

The given parameters:

Let the velocity of the pitcher = u₁

Apply the principle of conservation of linear momentum to determine the velocity of the pitcher as shown below;

m₁u₁ = m₂u₂

[tex]u_1 = \frac{m_2 u_2}{m_1} \\\\u_1 = \frac{0.15 \times 35}{50} \\\\u_1 = 0.105 \ m/s\\\\u_1 \approx 0.1 \ m/s[/tex]

Thus, the velocity of the pitcher at the given mass is 0.1 m/s.

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Answer:

This question assumes that the car accelerates at the same rate as when it went from 0 to 60km/h

24.29m/s or 87.4km/h

Explanation:

Let's find the acceleration of the car:

let vi=0, vf=60km/h (16.67m/s), Δt = 8.0s

a = (vf-vi)/Δt

a = (16.67m/s-0)/8.0

a = 2.08m/s^2

Now we can use this acceleration to find vf in the second part:

50km/h is 13.89m/s

a = (vf-vi)Δt

vf = aΔt + vi

vf = 2.08m/s^2*5.0+13.89m/s

vf = 24.29m/s (87.4km/h)

The half-life of the given isotope will be 10 days, if after 30 days only 31.25 grams are remaining from a sample of 250 grams of the sample size taken in the beginning.

The Half-life is the time which is required for a quantity to reduce the content to half of the amount present as its initial value. The term is used in nuclear physics to describe how quickly an unstable atom undergo radioactive decay or how long does stable atoms survive. The term is also used generally to characterize any type of exponential decay.

The half-life of the isotope can be calculated by the formula:

FR = 0.5n

FR = Fraction Remaining = 31.25 g / 250.0 g = 0.1250

n = number of half lives elapsed = ?

0.125 = 0.5n

log 0.125 = n log 0.5

-0.9031 = -0.3010 n

n = 3.000 half lives have elapsed

3 half lives = 30 days

1 half live = 10 days

Therefore, the half-life of the isotope will be 10 days.

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Assuming both billiard balls have the same mass, conservation of momentum says

[tex]m\vec v_1 + m\vec v_2 = m{\vec v_1}\,' + m{\vec v_2}\,'[/tex]

where m = mass of both billiard balls, and v₁ and v₂ = their initial velocities, and v₁' and v₂' = their final velocities. The masses are the same so the exact value of m is irrelevant. The first ball has initial speed 5 m/s and the second is at rest, so

[tex]\left(5 \dfrac{\rm m}{\rm s}\right) \, \vec\imath = {\vec v_1}\,' + {\vec v_2}\,'[/tex]

After the collision, the first ball has speed 4.35 m/s and is moving at angle of 30° below the original path, so

[tex]{\vec v_1}\,' = \left(4.35\dfrac{\rm m}{\rm s}\right)\left(\cos(30^\circ) \, \vec\imath + \sin(30^\circ) \, \vec\jmath\right) \approx \left(3.77 \dfrac{\rm m}{\rm s}\right) \vec\imath + \left(-2.18 \dfrac{\rm m}{\rm s}\right) \vec\jmath[/tex]

Then the second ball has final velocity vector

[tex]{\vec v_2}\,' \approx \left(1.23 \dfrac{\rm m}{\rm s}\right) \vec\imath + \left(2.18 \dfrac{\rm m}{\rm s}\right) \vec\jmath[/tex]

so it moves with speed

[tex]\left\|{\vec v_2}\,'\right\| \approx \sqrt{\left(1.23\dfrac{\rm m}{\rm s}\right)^2 + \left(2.18\dfrac{\rm m}{\rm s}\right)^2} \approx \boxed{2.50 \dfrac{\rm m}{\rm s}}[/tex]

at an angle of

[tex]\theta \approx \tan^{-1}\left(\dfrac{2.18}{1.23}\right) \approx \boxed{60.5^\circ}[/tex]

or about 60.5° above the original line of motion.

Explanation:

For the first question look at the picture. It should be pretty clear. Remember that cos45° = sqrt2 / 2.

2) We calculate it thanks to the conservation of mechanical energy:

Em1 = Em2

U1 + K1 = U2 + K2

K1 = 0J

U2 = 0j

U1 = K2

3) mgh = 1/2mv^2

v = sqrt(2gh)

Answer:

gunrun

Explanation:

Answer:

explorer

Explanation:

Answer:

a) EXPLORER

Explanation:

An explorer is someone who travels to new places or does new things.

Answer:

5 amps

Explanation:

I = P/V

I = current (amps)

P = power (watts)

V = voltage (volts)

I = 60/12

I = 5

Answer:

6 kg.m/s

Explanation:

Momentum is the product of mass and velocity. So,

Here,

→ p = 5 kg × 1.2 m/s

→ p = (5 × 1.2) kg.m/s

→ p = (5 × 12/10) kg.m/s

→ p = 12/2 kg.m/s

→ p = 6 kg.m/s

Therefore, momentum of the object is 6 kg.m/s.

The momentum of a 5kg object that has a velocity of 1.2m/s is 6.0kgm/s.

Momentum of a substance is the product of its mass and velocity. That is;

Momentum (p) = mass (m) × velocity (v)

According to this question, an object has a mass of 5kg and velocity of 1.2m/s. The momentum is calculated thus:

Momentum = 5kg × 1.2m/s

Momentum = 6kgm/s.

Therefore, the momentum of a 5kg object that has a velocity of 1.2m/s is 6.0kgm/s.

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Answer:

The speed.

Explanation:

The slope of a line is that line's rate of change.  If a car is travelling at 20 km/hr and we plot distance vs time graph, the slope of that line will be 20.

Answer:

C

Explanation:

A and B are not true and D is a disadvantage

Answer:

C.  Long-term cost savings for energy users.

Explanation:

C is correct because the first option is a drawback that is unlikely.  B is a good answer but not the best.  It's a likely benefit, but C is a more likely benefit.  D is a drawback.  C is correct.  I also got this right on my quiz.

Hope this helps!