Attached to the roof of a house are three solar panels, each 1 m x 2 m. Assume the equiv alent of 4 hrs of normally incident sunlight each day, and that all the incident light is absorbed and converted to heat. How many gallons of water can be heated from 40°C to 120°C each day?

Answer:

The force that acts on the man equals 15354.75 newtons.

Explanation:

After falling through a distance of 24.0 meters the speed of the stunt man upon hitting the mattress can be obtained using third equation of kinematics as

[tex]v^{2}=u^{2}+2gh\\\\\therefore v=\sqrt{2gh}\\\\v=\sqrt{2\times 9.81\times 24}\\\\v=21.7m/s[/tex] ( u=0 since the man falls from rest)

Now since the man is decelerated through a distance of 1.15 meters thus the acceleration produced can be obtained from third equation of kinematics as

[tex]v^{2}=u^{2}+2as\\\\0=u^{2}=2as\\\\a=\frac{-u^{2}}{2s}\\\\a=-\frac{(21.7^{2}}{2\times 1.15}=-204.73m/s^{2}[/tex]

Now by newton's second law the force that produced deceleration of the calculated magnitude is obtained as

[tex]F=mass\times acceleration\\\\F=75.0\times -204.73=-15354.75Newtons[/tex]

The negative sign indicates that the direction of force is opposite of motion.

Answer:

[tex]\Delta \lambda=4.94\times 10^{-13}\ m[/tex]

Explanation:

It is given that,

X-rays are scattered from a target at an angle of, [tex]\theta=37.2^{\circ}[/tex]

We need to find the wavelength shift of the scattered x-rays. The shift in wavelength is given by :

[tex]\Delta \lambda=\dfrac{h}{mc}(1-cos\ \theta)[/tex]

h is the Planck's constant

m is the mass of electron

c is the speed of light

[tex]\Delta \lambda=\dfrac{6.63\times 10^{-34}}{9.1\times 10^{-31}\times 3\times 10^8}(1-cos(37.2))[/tex]

[tex]\Delta \lambda=4.94\times 10^{-13}\ m[/tex]

So, the wavelength shift of the scattered x- rays is [tex]4.94\times 10^{-13}\ m[/tex]. Hence, this is the required solution.

Answer:

The average speed is less than 70 km/h.

(B) is correct option.

Explanation:

Given that,

distance = 6.0 km

Speed = 50 km/h

Speed = 90 km/h

We need to calculate the time in 6.0 km distance

Using formula of time

[tex]t = \dfrac{d}{v}[/tex]

Put the value in to the formula

[tex]t=\dfrac{6.0}{50}[/tex]

[tex]t=0.12\ hr[/tex]

We need to calculate the time in another distance

Using formula of time

[tex]t = \dfrac{d}{v}[/tex]

Put the value in to the formula

[tex]t=\dfrac{6.0}{90}[/tex]

[tex]t=0.067\ hr[/tex]

We need to calculate the average speed

Using formula of average speed

[tex]v=\dfrac{D}{T}[/tex]

Where, D = total distance

T = total time

Put the value into the formula

[tex]v=\dfrac{12}{0.12+0.067}[/tex]

[tex]v=64.17\ km/hr[/tex]

Hence, The average speed is less than 70 km/h.

The average speed over the 12 km drive is less than 70 km/h since the total time for the trip is 0.187 hours, leading to an average speed of 64.2 km/h.

To calculate the average speed for the entire trip, you must divide the total distance by the total time taken. In the given scenario, you drive 6.0 km at 50 km/h and then another 6.0 km at 90 km/h. First, calculate the time taken for each portion of the trip.

Now, add the times together and divide the total distance by the total time to find the average speed.

Therefore, the average speed over the 12 km drive is less than 70 km/h, which corresponds to option (B).

Answer:

Change in momentum is [tex]2.667\times 10^{4} kg.m/s[/tex]

Solution:

The momentum of any body is the product of its mass and the velocity associated with the body and is generally given by:

[tex]\vec{p} = m\vec{v}[/tex]

Now, as per the question:

Mass of the car, M = 1500 kg

The velocity in the east direction, [tex]v\hat{i} = 40\hat{i} km/h[/tex]

The velocity in the north direction, [tex]v\hat{j} = 50\hat{j} km/h[/tex]

Now, the momentum of the car in the east direction:

[tex]p\hat{i} = mv\hat{i} = 1500\times 40\hat{i} = 60000\hat{i} kg.km/h[/tex]

Now, the momentum of the car in the north direction:

[tex]p\hat{j} = mv\hat{j} = 1500\times 50\hat{j} = 75000\hat{j} kg.km/h[/tex]

Change in momentum is given by:

[tex]\Delta p = p\hat{i} - p\hat{j} = 60000\hat{i} - 75000\hat{j}[/tex]

Now,

[tex]|\Delta p| = |60000\hat{i} - 75000\hat{j}|[/tex]

[tex]|\Delta p| = \sqrt{60000^{2} + 75000^{2}}[/tex]

[tex]|\Delta p| = 96046 kg.km/hr = \frac{96046}{3.6} = 2.667\times 10^{4} kg.m/s[/tex]

(Since, [tex]1kg.km/h = \frac{1}{3.6} kg.m/s[/tex])

Answer:

21 m/s

Explanation:

For the first ball, in the x direction:

x = x₀ + v₀ t + ½ at²

x = 0 + (8.2 cos 35) t + ½ (0) t²

x = 6.72t

In the y direction:

y = y₀ + v₀ t + ½ at²

y = 8 + (8.2 sin 35) t + ½ (-9.8) t²

y = 8 + 4.70t − 4.9t²

When y = 4:

4 = 8 + 4.70t − 4.9t²

4.9t² − 4.70t − 4 = 0

Solve for t with quadratic formula:

t = [ 4.70 ± √((-4.70)² − 4(4.9)(-4)) ] / 9.8

t = (4.70 ± 10.0) / 9.8

t = 1.50

Therefore:

x = 6.72t

x = 10.1

Now, for the second ball in the x direction:

x = x₀ + v₀ t + ½ at²

x = 0 + (v₀ cos (-θ)) (t − 1) + ½ (0) (t − 1)²

x = v₀ cos θ (t − 1)

And in the y direction:

y = y₀ + v₀ t + ½ at²

y = 8 + (v₀ sin (-θ)) (t − 1) + ½ (-9.8) (t − 1)²

y = 8 − v₀ sin θ (t − 1) − 4.9(t − 1)²

When t = 1.50, x = 10.1 and y = 4:

10.1 = v₀ cos θ (1.50 − 1)

v₀ cos θ = 20.1

4 = 8 − v₀ sin θ (1.50 − 1) − 4.9(1.50 − 1)²

4 = 6.76 − 0.50 v₀ sin θ

v₀ sin θ = 5.49

Using Pythagorean theorem:

v₀² = (v₀ cos θ)² + (v₀ sin θ)²

v₀² = (20.1)² + (5.49)²

v₀ = 20.8

Rounded to two significant figures, the required initial speed is 21 m/s.

Answer:

39.56 x 10⁻² V

Explanation:

Peak emf in a rotating coil

= n BAω

Where n is no of turns of coil , B is magnetic field , A is area of coil and ω is angular velocity of rotation of coil

Here n = 1

B = .21 T

A = 5 X 12 X 10⁻⁴ = 60 X 10⁻⁴

ω = 2π X 50 = 100π

Emf = 1 x .21 x 60 x 10⁻⁴ x 100 x 3.14

=  39.56 x 10⁻² V

Answer: the fraction is [tex]0.88*10^{-6}[/tex]

Explanation:

Hi!

The land area per capita in USA is 28,310 square km. Then the solar power per capita is (rounding some numbers):

[tex]P_s = 300 \frac{W}{m^2} (28,310) km^2 =  3*10^2*2.83*10^4*10^6 W = 8.49*10^{12} W = 8.49*10^9 kW[/tex]

If we take 20% of this power, the fraction k to have 1.5 kW is:

[tex]1.5 kW = k(0.2*8.49 * 10^9 kW)[/tex]

[tex]k = \frac{1.5}{1.7}*10^{-6} = 0.88 *10^{-9} [/tex]

Final answer:

To answer the question, we need to calculate the total electrical energy consumption in the U.S., understand the solar energy per square meter, consider the 20% efficiency of solar cells, and determine the needed land area for solar panels to meet the country's electrical energy needs.

Explanation:

The question involves calculating what fraction of the United States' land area would need to be covered with 20% efficient solar cells to provide all of its electricity, given that the average American uses electricity at the rate of about 1.5 kW and solar energy reaches the Earth's surface at an average rate of about 300 watts per square meter. To find this fraction, we first need to consider the total electrical energy consumption of the United States and then assess how much of this demand can be met by the solar energy available on a given area of land, taking into consideration the efficiency of the solar cells.

The key steps include calculating the total power used by Americans in watts, understanding the energy provided by the sun per square meter, adjusting for the efficiency of solar conversion, and finally, determining the land area required. Specifically, a 20% conversion efficiency means that only a fifth of the solar energy striking the solar cells is converted into usable electrical energy. With these considerations, the solution entails a mix of energy requirement calculations and solar energy potential assessments to identify the required land area for solar panels.

Final answer:

The frequency of the wave is 1075 Hz, and the wavelength is 0.08 m. The wave equation of the form y(x, t) = ym sin(kx ± ωt + φ) represents a sinusoidal wave with specific parameters. The amplitude is 0.04 m, the wave number is 25π m⁻¹, the angular frequency is 6755π rad/s, and the phase angle can be either +π or -π. The choice of sign in front of ω determines the direction of wave propagation.

Explanation:

To find the frequency of the wave, we can use the formula f = v/λ, where f is the frequency, v is the speed of the wave, and λ is the wavelength. In this case, the speed of the wave is given as 86 m/s. Since the wave is sinusoidal, the wavelength is equal to twice the amplitude of the transverse displacement of the string particle at x = 0. So, the wavelength is equal to 2 times 4.0 cm, which is 8.0 cm or 0.08 m.

Substituting these values into the formula, we get f = 86 m/s / 0.08 m = 1075 Hz. Therefore, the frequency of the wave is 1075 Hz.

To find the wavelength of the wave, we can use the formula λ = v/f, where λ is the wavelength, v is the speed of the wave, and f is the frequency. Substituting the given values, we get λ = 86 m/s / 1075 Hz = 0.08 m.

Therefore, the wavelength of the wave is 0.08 m.

The wave equation of the form y(x, t) = ym sin(kx ± ωt + φ) represents a sinusoidal wave. In this equation, ym is the amplitude of the wave, k is the wave number, ω is the angular frequency, and φ is the phase angle. The choice of the sign in front of ω determines the direction of wave propagation. If it is positive, the wave propagates in the positive x-direction, and if it is negative, the wave propagates in the negative x-direction.

In this case, the amplitude of the wave is given as 4.0 cm or 0.04 m. The wave number can be calculated using the formula k = 2π/λ, where k is the wave number and λ is the wavelength. Substituting the given wavelength of 0.08 m, we get k = 2π/0.08 m = 25π m⁻¹.

The angular frequency can be calculated using the formula ω = 2πf, where ω is the angular frequency and f is the frequency. Substituting the given frequency of 1075 Hz, we get ω = 2π × 1075 Hz = 6755π rad/s.

The phase angle is given as ± π. The choice between +π and -π determines the phase of the wave at x = 0 and t = 0.

Therefore, (c) ym = 0.04 m, (d) k = 25π m⁻¹, (e) ω = 6755π rad/s, (f) φ = ±π, and (g) the correct choice of sign in front of ω depends on the desired direction of wave propagation.

Answer:

The horizontal distance is 2.41 mts

Explanation:

For this problem, we will use the formulas of parabolic motion.

[tex]Y=Yo+Voy*t+\frac{1}{2}*a*t^2\\Vx=V*cos(\alpha)\\Vy=V*sin(\alpha)[/tex]

We need to find the time of the whole movement (t), for that we will use the first formula:

we need the initial velocity for that:

[tex]Vy=4.4*sin(24^o)\\Vy=1.79m/s[/tex]

so:

[tex]0=0.70+1.79*t+\frac{1}{2}*(-9.8)*t^2[/tex]

now we have a quadratic function, solving this we obtain two values of time:

t1=0.60sec

t2=-0.234sec

the obvious value is 0.60sec, we cannot use a negative time.

Now we are focusing on finding the horizontal distance.

the movement on X is a constant velocity motion, so:

[tex]x=Vx*t[/tex]

[tex]Vx=4.4*cos(24^o)=4.02m/s\\[/tex]

so:

[tex]x=4.02*(0.60)=2.41m[/tex]

Final answer:

To find the shortest time for the passing maneuver, we must consider the car's acceleration and deceleration phases and the distance to be traveled. The task involves calculations using the kinematic equations for uniformly accelerated motion.

Explanation:

To calculate the shortest time in which the driver of the car can complete the passing operation, we must consider the car's acceleration, maximum speed, and the distance to be covered. The car must not only reach a point 40 feet in front of the truck but also get back to the speed of 35 mi/h after overtaking, all while not exceeding a speed of 50 mi/h. The entire maneuver consists of accelerating to the maximum speed, maintaining that speed for a portion of the pass, and then decelerating back to 35 mi/h.

First, convert speeds from miles per hour to feet per second:

35 mi/h = 51.33 ft/s (approximately),

50 mi/h = 73.33 ft/s (approximately).

The car needs to cover an initial 40 ft behind the truck and a further 40 ft to be ahead, for a total of 80 ft. We would calculate the time needed to accelerate to 50 mi/h (maximum passing speed), the time spent traveling at this top speed, and then the time to decelerate back to 35 mi/h, all while covering the required distance. The actual calculations involve using the kinematic equations for uniformly accelerated motion; however, without further details on the constraints such as road length, traffic laws, and exact acceleration and deceleration phases, a precise number cannot be produced.

Answer:

The given statement is false.

Explanation:

For any negative vector

[tex]\overrightarrow{r}=-x\widehat{i}-y\widehat{j}[/tex]

The magnitude of the vector is given by

[tex]|r|=\sqrt{(-x)^{2}+(-y)^{2}}\\\\|r|=\sqrt{x^2+y^2}[/tex]

As we know that square root of any quantity cannot be negative thus we conclude that the right hand term in the above expression cannot be negative hence we conclude that magnitude of any vector cannot be negative.

Answer: Hi!

The acceleration of our particle is then a = 4*[tex]10^{3[/tex] meters per second square. Also we know that we start at X₀ = O m (i am not sure if you are using a a 0 or a O, but you will see that in this problem it doesn't matter, se i will use a constant O, that can be  ani real number as the initial position) and V₀ = 0 m/s.

Ok, we have the acceleration, so if we want the velocity, we must integrate the acceleration over time.

V(t) = ∫ 4*[tex]10^{3[/tex]dt = 4*[tex]10^{3[/tex]*t + V₀

where we added the constant of integration, who is the inicial velocity, that we already know that is zero.

and for the position, we must integrate again.

X(t) =  ∫ 4*[tex]10^{3[/tex]*tdt =  4*[tex]10^{3[/tex]*[tex]t^{2}[/tex]/2 + X₀

ok, in the part a) we want to know the displacement at 2 seconds.

that is X(2s) - X(0s) = (2000*4 + O) - O meters = 8000 meters.

in the b part we want to know the velocity at 1 second; that is:

V(1s) = 4000*1 m/s = 4000 meters per second.

Answer:

[tex]f_{ecco}  = 360 Hz[/tex]

Explanation:

The change of frecuency of sound due to the movement of the source is colled Doppler Effect.

As James (the source) is running toward the wall, the frecuency reaching the wall (so the eco sound) will be higher than the source. In this case the frecuency at the wall will be:

[tex]f_{2}  = f_{1}  (\frac{v}{v-v_{s} } )[/tex]

where [tex]v_{s}[/tex] is the speed of source, 2 m/s

and [tex]v[/tex] is the speed of sound, given that we have wind movind the air in the opposite direction respect to the wall, the speed of sound would be:

[tex]v = 350 \frac{m}{s} - 3 \frac{m}{s} = 347 \frac{m}{s}[/tex]

Replacing the values: [tex]f_{2}  = 357 Hz[/tex]

Now the wall becames the new source, and James (the observer is aproaching the source), for an observer aproaching the source the new frecuency will be:

[tex]f_{3}  = f_{2}  (1 + \frac{v_{s}}{v} )[/tex]

Now the waves are traveling in the direction of wind, so the velocity of sound will be:

[tex]v = 350 \frac{m}{s} + 3 \frac{m}{s} = 353 \frac{m}{s}[/tex]

Replacing:

[tex]f_{3}  = 360 Hz[/tex]

Answer:

virtual the image is virtual because image formed viruvirualconvex mirror

Answer:

Speed of ball equals 6.024 m/s.

Explanation:

Let the student throw the ball with a velocity of 'v' m/s horizontally.

Now the time in which the ball travels 10.0 meter horizontally shall be equal to the time in which it travels (15.0-1.50) meters vertically

Hence the time taken to cover a vertical distance of 13.50 meters is obatined using 2 equation of kinematics as

[tex]s=\frac{1}{2}gt^{2}\\\\t=\sqrt{\frac{2s}{g}}\\\\t=\sqrt{\frac{2\times 13.5}{9.81}}\\\\\therefore t=1.66 seconds[/tex]

Since there is no acceleration in horizantal direction we infer that in time of 1.66 seconds the ball travels a distance of 10 meters

Hence the spped of throw is obatines as

[tex]Speed=\frac{Distance}{Time}\\\\v=\frac{10}{1.66}=6.024m/s[/tex]

Final answer:

The initial speed of the softball can be calculated using the height it drops and the horizontal distance it travels. By determining the time of fall for the vertical drop and knowing the horizontal distance, the initial horizontal velocity can be found, approximately 6.02 m/s.

Explanation:

To solve for the initial speed of the softball, we need to analyze the motion in two dimensions separately: horizontal and vertical.

Horizontal Motion

The horizontal motion can be considered with constant velocity since there's no acceleration in that direction (ignoring air resistance).

Vertical Motion

The vertical motion can be described by the kinematic equations for uniformly accelerated motion (free fall). Given the height difference from the window to the catchpoint (13.5 m) and the acceleration due to gravity (9.81 m/s²), we can calculate the time it takes for the ball to fall this height. The equation we use is:

h = vit + (1/2)at²

Substitute h = 13.5 m, a = 9.81 m/s², and vi = 0 m/s (since the ball is thrown horizontally, the initial vertical speed is 0) to solve for t.

We find that the time t is approximately 1.66 seconds. Using this time and the horizontal distance of 10.0 m, we can now calculate the initial horizontal speed.

vh = d/t

Substituting d = 10.0 m and t = 1.66 s, the initial horizontal speed vh is approximately 6.02 m/s.

Answer:

F = 104.832 N

Explanation:

given,

upward acceleration of the lift = 1.90 m/s²

mass of box containing new computer = 28 kg.

coefficient of friction = 0.32

magnitude of force = ?

box is moving at constant speed hence acceleration will be zero.

Now force acting due to lift moving upward =

               F = μ m ( g + a )

               F = 0.32 × 28 × ( 9.8 + 1.9 )

              F = 104.832 N

hence, the force applied should be equal to 104.832 N

Answer:

Number of gallons =2 gallon

Explanation:

given data:

rate of gasoline ineurope = 5 euro per liter

total money to buy gasoline =  40 euro

total gasoline an american can buy in europe [tex]= \frac{40}{5}[/tex]

= 8 litres of gasoline

As given in the question 1 ltr is 1 quarts therefore  

Total no. of quarts is 8 quarts

As from question 4 quarts is equal to one gallon, hence

Number of gallons[tex]= \frac{8}{4} = 2 gallon[/tex]

Answer:

490hp

Explanation:

Power is energy per unit of time, an in this case the energy needed is the gravitational potential energy, so we have:

[tex]P=E/t=mgh/t=(3730kg)(9.8m/s)(600m)/60s=365540W[/tex]

Since all units are in S.I. we get our result in Watts (Joules/s). To convert to horse power (imperial), we need to know that:

[tex]745.7 W = 1 hp[/tex]

Which obviously means:

[tex]\frac{1 hp}{745.7 W} = 1[/tex]

So we can write:

[tex]P=365540W=365540W(\frac{1 hp_m}{745.7 W})=490hp[/tex]

There is also metric horse power ([tex]735.5 W = 1 hp[/tex]), and using this value we get [tex]P=497hp[/tex], although both results are close.

Final answer:

To calculate the SUV's power output, we find the work done against gravity and divide it by the time taken to get power in watts. This is then converted to horsepowers leading to the answer of 490 hp. The correct answer is b) 490 hp.

Explanation:

To find the power output in horsepowers of the 3730-kg SUV climbing a 600-meter hill in 60 seconds, first we calculate the work done against gravity, which is equal to the force due to gravity (weight of the SUV) multiplied by the height of the hill:

Work = Weight × Height = (mass × gravity) × height

Then, we convert the weight to newtons by multiplying the mass (kg) by the acceleration due to gravity (9.81 m/s2, approximately), and multiply that result by the height (in meters).

Power in watts is calculated by dividing the work done by the time taken in seconds:

Power (W) = Work done (Joules) / Time (seconds)

To convert watts to horsepowers, we use the conversion rate where 1 horsepower is equivalent to 746 watts:

Power (hp) = Power (W) / 746

After plugging in the values, the SUV's power output in horsepowers would be:

Power (W) = (3730 kg × 9.81 m/s2) × 600 m / 60 s = 365,130 W

Power (hp) = 365,130 W / 746 = 489.43 hp, which we round to 490 hp.

Thus, the correct answer from the given options is 490 hp.

Answer:

acceleration = 0.8181 m/s²

Explanation:

given data

mass = 1.1 kg

apart d = 1 m

charge q = 10 μC

to find out

What is the initial acceleration

solution

we know that acceleration is

acceleration = [tex]\frac{force}{mass}[/tex]   .................1

here force = [tex]k \frac{q1q2}{r^2}[/tex]

here q1 q2 is charge and r is distance and Coulomb constant k = 9 × [tex]10^{9}[/tex] Nm²/C²

force = [tex]9*10^{9} \frac{(10*10^{-6})^2}{1^2}[/tex]

force = 0.9 N

so  from equation 1

acceleration = [tex]\frac{0.9}{1.1}[/tex]

acceleration = 0.8181 m/s²

Answer:

Explanation:

Gas law equation for any gas is as follows .

PV = nRT ( for n moles of gas )

Let the pressure , volume , temperature and mole of gas in cylinder A be P,V

T₁ and 2n . Pressure , volume , temperature and mole in cylinder B will be

P , V , T₂ and n.

Applying Gas laws , we get

For gas in cylinder A

PV = 2n R T₁

For gas in cylinder B

PV = n R T₂

Equating these equations , we get

2n R T₁ = n R T₂

2 T₁ = T₂

or,

[tex]2T_A =T_B[/tex]

[tex]T_A[/tex] is less than [tex]T_B[/tex]

Final answer:

Under the conditions of equal pressure and volume, and using the ideal gas law, we determine that the temperatures of the two cylinders of gas must be the same (TA = TB).

Explanation:

Given that the two identical cylinders, A and B, contain the same type of gas at the same pressure, and cylinder A has twice as much gas as cylinder B, we can use the ideal gas law to determine the relationship between their temperatures. The ideal gas law is PV = n ×R× T, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. Since the pressures are equal and the cylinders are identical, volumes are also equal. Thus, because A has twice as much gas as B (nA = 2 x nB), it has twice the number of moles. Holding pressure and volume constant and since R is a constant, both cylinders must have the same temperature for the equation to be balanced. Therefore, we find that TA = TB.

Answer:

24.325 kg m/s

Explanation:

Initial momentum, pi = 18 kg m/s

F = < -4, 12, 0>

t = 0.5 s

Let the final momentum is pf.

The magnitude of force is

[tex]F=\sqrt{(-4)^{2}+12^{2}+0^{2}}=12.65 N[/tex]

According to the Newton's second law, the rate of change of momentum is equal to the force.

[tex]F = \frac{p_{f}-p_{1}}{t}[/tex]

[tex]12.65= \frac{p_{f}-18}}{0.5}[/tex]

pf - 18 = 6.325

pf = 24.325 kg m/s

Thus, the momentum of body after 0.5 s is 24.325 kg m/s.

Answer:

How: It will have a very different chemical composition.

Why: Because the interstellar medium at the beginning of universe were compounded only of Hydrogen and Helium.

Explanation:

Once the Big Bang passed and the universe began its expansion, the temperature started to decrease, what allowed the combination of hydrogen and helium. Therefore, the chemical composition of the molecular cloud in which the first stars were formed only held those elements.

If the Sun and the solar system were formed from a molecular cloud with that composition, it will both have an absence of metallic elements (elements heavier than helium), since all of them are formed through nuclear reactions in the core of the stars, and each time a star dies, the interstellar medium for the next generation is enriched.

Key elements for life as Carbon, Nitrogen, Oxygen, Phosphorus and Sulfur will be missing for that hypothetical scenario.

For example, the lack of O3 (ozone) in the atmosphere of earth will allow that ultraviolet light hits the earth surface.

If our solar system formed with the first stars, the planets would mostly comprise hydrogen and helium, as heavier elements had not yet formed. The conditions would be hotter and harsher, making life as we know it unlikely to evolve. The Sun, too, would've been exhausted already due to its short lifespan.

If our Sun and the solar system had formed around the same time as the first stars in the universe, our solar system would look very different. The universe at the time of the formation of the first stars was composed of only hydrogen and helium, with trace amounts of lithium. Thus, the planets in our system, formed from the leftover dust and gasses surrounding our Sun, would mostly be made up of hydrogen and helium.

Believed to have occurred just about 200 million years after the big bang, the first stars were much larger and hotter than the current generation of stars, including our Sun. Hence, the planets in our system could have been significantly hotter and larger. It's also worth noting that these first-generation stars had relatively short lifetimes and ended their lives in explosive supernovae, catalyzing the formation of heavier elements. But this means if our Sun was a first-generation star, it would have exhausted its nuclear fuel billions of years ago.

Due to these circumstances, life as we know it might not have been possible in our solar system. Life on Earth relies on heavier elements like carbon, nitrogen, and oxygen, which were only formed in the universe after generations of stellar evolution and supernova explosions. If our solar system was created at the same time as the first stars, these heavier elements wouldn't have existed yet. Therefore, life, at least life as we understand it, wouldn't likely evolve in our solar system.

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Answer:

4.51 * 10^{-5} C

Explanation:

The force between two charge  q and q1 is given as

[tex]F = \frac{k*q*q1}{r^2}[/tex]

[tex]= \frac{(9.0 * 10^9)(24 * 10^{-6})(8 * 10^{-6} C)}{(0.19m)^2} [/tex]

= 47.86 N in the +y direction

We need the force between q and q2 to be (47.86 - 18) =  29.86 N in the other direction to get the desired result.

solving for q2,

[tex]q2 = \frac{Fr^2}{(kq)} [/tex]

[tex]= \frac{(29.86)(0.33 m)^2}{(9.0 * 10^9*8*10^{-6} C)}[/tex]

[tex]= 4.51 * 10^{-5} C[/tex]

Final answer:

To determine the magnitude of q2, we can use Coulomb's Law to calculate the net force exerted on charge q. By setting up an equation using the given information, we can find that the magnitude of q2 is approximately 4.84 μC.

Explanation:

To determine the magnitude of q2, we can use Coulomb's Law, which states that the electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, we have two charges, q1 and q2, with a distance of 0.33 - 0.19 = 0.14m between them.

The net electrostatic force on charge q can be calculated using the equation F = k * (|q1 * q| / r1^2) + k * (|q2 * q| / r2^2), where k is the electrostatic constant (8.99 x 10^9 N*m^2/C^2).

From the given information, we know that F = 18 N and points in the +y direction, so we can set up the following equation: 18 = k * (|(-24 μC) * (8 μC)| / (0.19m)^2) + k * (|q2 * (8 μC)| / (0.33m)^2).

Solving this equation, we can find the magnitude of q2, which is approximately 4.84 μC.

Explanation:

There are two components of a longitudinal sound wave which are compression and rarefaction. Similarly, there are two components of the transverse wave, the crest, and trough.

The crest of a wave is defined as the part that has a maximum value of displacement while the trough is defined as the part which corresponds to minimum displacement.

While compression is that space where the particles are close together while the rarefaction is that space where the particles are far apart from each other.

So, the refraction or the rarefied part of a longitudinal sound wave is analogous to a trough of a transverse wave.  

Answer:

[tex]a=\frac{v_{f}-v_{o}  }{t_{f}-t_{o}  } =\frac{(7-22)\frac{m}{s} }{5s-0s} =-3\frac{m}{s^{2} }[/tex]

Explanation:

We know that the initial velocity is 22 m/s

The final velocity after applying the brakes is 7 m/s, and the time that takes it to break is 5 seconds

We know that the concept of acceleration is the change of velocity in time

[tex]a=\frac{v_{f}-v_{o}  }{t_{f}-t_{o}  } =\frac{(7-22)\frac{m}{s} }{5s-0s} =-3\frac{m}{s^{2} }[/tex]

The answer is negative since the car is slowing down  

Answer:Momentum of Truck[tex]=4000\times 20=80,000 kg-m/s[/tex]

Momentum of car[tex]=1350\times 10=13,500 kg-m/s[/tex]

Explanation:

Given

mass of truck(m)=4000 kg

Velocity of Truck is ([tex]V_T[/tex])=[tex]-20\hat{j}[/tex]

mass of car ([tex]m_c[/tex])=1350 kg

Velocity of car[tex](V_c)=10 \hat{j}[/tex]

Conserving momentum

[tex]4000\times \left ( -20\right )+1350\left ( 10\right )=5350v[/tex]

[tex]v=\frac{66,500}{5350}=12.42 m/s[/tex]

Momentum of Truck[tex]=4000\times 20=80,000 kg-m/s[/tex]

Momentum of car[tex]=1350\times 10=13,500 kg-m/s[/tex]

Answer:

1) Momentum of truck before collision is [tex]\overrightarrow{p_{1}}=-80000kgm/s[/tex]

2) Momentum of car before collision is [tex]\overrightarrow{p_{2}}=13500kgm/s[/tex]

Explanation:

The momentum of an object with mass 'm' travelling with speed 'v' is mathematically given by

[tex]\overrightarrow{p}=mass\times \overrightarrow{v}[/tex]

In this problem we shall assume that direction's coincide with the Cartesian axis for simplicity

Thus for Truck we have

Mass = 4000 kg

Velocity = [tex]-20\widehat{j}[/tex]m/s

Thus momentum of truck becomes

[tex]\overrightarrow{p_{1}}=4000\times -20\overrightarrow{j}=-80000kgm/s[/tex]

Similarly for car we have

Mass = 1350 kg

Velocity = [tex]10\widehat{j}[/tex]m/s

Thus momentum of car becomes

[tex]\overrightarrow{p_{2}}=1350\times 10\overrightarrow{j}=13500kgm/s[/tex]

Answer:

The correct option is 'c': Decreases.

Explanation:

As we know that when we throw a ball upwards we imoart a kinetic energy to the bsll. As the ball moves upwards the kinetic energy of the ball starts to decrease as the ball slows down as it moves upwards as work has to be done for movement against gravity. This work done against gravity is stored as potential energy of the ball.

Mathematically as we throw the ball upward's with velocity 'u' it's initial kinetic energy equals [tex]E_{initial}=\frac{1}{2}mu^{2}[/tex]

As the ball attain's a height 'h' it's total energy is sum of the potential and the remaining kinetic energy as follows

[tex]E(h)=mgh+\frac{1}{2}mv^{2}[/tex]

Equating both the energies we get

[tex]\frac{1}{2}mu^{2}=mgh+\frac{1}{2}mv^{2}\\\\\\therefore v=\sqrt{u^{2}-2gh}[/tex]

Hence we can see as the height increases the velocity decreases.

Answer:

The amount of energy required is [tex]152.68\times 10^{3}Joules[/tex]

Explanation:

The energy required to convert the ice to steam is the sum of:

1) Energy required to raise the temperature of the ice from -20 to 0 degree Celsius.

2) Latent heat required to convert the ice into water.

3) Energy required to raise the temperature of water from 0 degrees to 100 degrees

4) Latent heat required to convert the water at 100 degrees to steam.

The amount of energy required in each process is as under

1) [tex]Q_1=mass\times S.heat_{ice}\times \Delta T\\\\Q_1=50\times 2.05\times 20=2050Joules[/tex]

where

[tex]'S.heat_{ice}[/tex]' is specific heat of ice =[tex]2.05J/^{o}C\cdot gm[/tex]

2) Amount of heat required in phase 2 equals

[tex]Q_2=L.heat\times mass\\\\\therefore Q_{2}=334\times 50=16700Joules[/tex]

3) The amount of heat required to raise the temperature of water from 0 to 100 degrees centigrade equals

[tex]Q_3=mass\times S.heat\times \Delta T\\\\Q_1=50\times 4.186\times 100=20930Joules[/tex]

where

[tex]'S.heat_{water}[/tex]' is specific heat of water=[tex]4.186J/^{o}C\cdot gm[/tex]

4) Amount of heat required in phase 4 equals

[tex]Q_4=L.heat\times mass\\\\\therefore Q_{4}=2260\times 50=113000Joules\\\\[/tex][tex]\\\\\\\\[/tex]Thus the total heat required equals [tex]Q=Q_{1}+Q_{2}+Q_{3}+Q_{4}\\\\Q=152.68\times 10^{3}Joules[/tex]

It would take 200 kJ of energy to completely vaporize the ice cube.

The process of completely vaporizing an ice cube can be broken down into four separate steps, each requiring a certain amount of energy:

In total, it would take 200 kJ of energy to completely vaporize the ice cube.

Answer:

[tex]3.75*10^{-13}[/tex]  electrons

Explanation:

The total charge Q is the sum of the charge of the N electrons contained in the sphere:

[tex]Q=N*q_{e}[/tex]

[tex]q_{e}=-1.6*10^{-19}C[/tex]    charge of a electron

We solve to find N:

[tex]N=\frac{Q}{q_{e}}=\frac{-6 x 10^{-6}}{-1.6 x 10^{-19}}=3.75*10^{-13}[/tex]

Answer:Displacement =69 km

Explanation:

Given

First John notices 245 km marker i.e. he is 245 away from destination.

John travels until he reach 135 km marker i.e. he is 135 km away from destination.

After that he retraces his path to reach 176 km marker

so his resultant displacement is i.e. shortest distance between initial and final point is 245-176 =69 km